Vladimir Gilelevich Maz'ya (russian: Владимир Гилелевич Мазья; born 31 December 1937)
[See .][See , , and .] (the
family name
In some cultures, a surname, family name, or last name is the portion of one's personal name that indicates one's family, tribe or community.
Practices vary by culture. The family name may be placed at either the start of a person's full name ...
is sometimes
transliterated
Transliteration is a type of conversion of a text from one script to another that involves swapping letters (thus '' trans-'' + '' liter-'') in predictable ways, such as Greek → , Cyrillic → , Greek → the digraph , Armenian → or ...
as Mazya, Maz'ja or Mazja) is a
Russia
Russia (, , ), or the Russian Federation, is a List of transcontinental countries, transcontinental country spanning Eastern Europe and North Asia, Northern Asia. It is the List of countries and dependencies by area, largest country in the ...
n-born
Swedish
Swedish or ' may refer to:
Anything from or related to Sweden, a country in Northern Europe. Or, specifically:
* Swedish language, a North Germanic language spoken primarily in Sweden and Finland
** Swedish alphabet, the official alphabet used by ...
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
, hailed as "one of the most distinguished analysts of our time" and as "an outstanding mathematician of worldwide reputation", who strongly influenced the development of
mathematical analysis
Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (m ...
and the
theory of partial differential equations.
Mazya's early achievements include: his work on
Sobolev space
In mathematics, a Sobolev space is a vector space of functions equipped with a norm that is a combination of ''Lp''-norms of the function together with its derivatives up to a given order. The derivatives are understood in a suitable weak sense t ...
s, in particular the discovery of the equivalence between
Sobolev and
isoperimetric/isocapacitary inequalities (1960), his counterexamples related to
Hilbert's 19th and
Hilbert's 20th problem (1968), his solution, together with
Yuri Burago
Yuri Dmitrievich Burago (russian: Ю́рий Дми́триевич Бура́го) (born 1936) is a Russian mathematician. He works in differential geometry, differential and convex geometry.
Education and career
Burago studied at Saint Pete ...
, of a problem in
harmonic potential theory (1967) posed by , his extension of the
Wiener regularity test to –Laplacian and the proof of its sufficiency for the boundary regularity. Maz'ya solved
Vladimir Arnol'd
Vladimir Igorevich Arnold (alternative spelling Arnol'd, russian: link=no, Влади́мир И́горевич Арно́льд, 12 June 1937 – 3 June 2010) was a Soviet and Russian mathematician. While he is best known for the Kolmogorov–A ...
's problem for the
oblique derivative boundary value problem (1970) and
Fritz John
Fritz John (14 June 1910 – 10 February 1994) was a German-born mathematician specialising in partial differential equations and ill-posed problems. His early work was on the Radon transform and he is remembered for John's equation. He was a 1 ...
's problem on the oscillations of a fluid in the presence of an immersed body (1977).
In recent years, he proved a
Wiener's type criterion for higher order elliptic equations, together with
Mikhail Shubin solved a problem in the spectral theory of the
Schrödinger operator formulated by
Israel Gelfand
Israel Moiseevich Gelfand, also written Israïl Moyseyovich Gel'fand, or Izrail M. Gelfand ( yi, ישראל געלפֿאַנד, russian: Изра́иль Моисе́евич Гельфа́нд, uk, Ізраїль Мойсейович Гел ...
in 1953, found
necessary and sufficient condition
In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements. For example, in the conditional statement: "If then ", is necessary for , because the truth of ...
s for the validity of
maximum principle
In the mathematical fields of partial differential equations and geometric analysis, the maximum principle is any of a collection of results and techniques of fundamental importance in the study of elliptic and parabolic differential equations.
...
s for elliptic and
parabolic systems of PDEs and introduced the so–called
approximate approximations. He also contributed to the development of the
theory of capacities,
nonlinear potential theory, the
asymptotic
In analytic geometry, an asymptote () of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the ''x'' or ''y'' coordinates tends to infinity. In projective geometry and related contexts, ...
and
qualitative theory of arbitrary order elliptic equations, the
theory of ill-posed problems, the theory of
boundary value problem
In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions. A solution to a boundary value problem is a solution to t ...
s in
domains with piecewise smooth
boundary
Boundary or Boundaries may refer to:
* Border, in political geography
Entertainment
*Boundaries (2016 film), ''Boundaries'' (2016 film), a 2016 Canadian film
*Boundaries (2018 film), ''Boundaries'' (2018 film), a 2018 American-Canadian road trip ...
.
Biography
Life and academic career
Vladimir Maz'ya was born on 31 December 1937
in a Jewish family.
[See .] His father died in December 1941 at the
World War II
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...
front
Front may refer to:
Arts, entertainment, and media Films
* ''The Front'' (1943 film), a 1943 Soviet drama film
* ''The Front'', 1976 film
Music
* The Front (band), an American rock band signed to Columbia Records and active in the 1980s and e ...
,
[See .] and all four grandparents died during the
siege of Leningrad
The siege of Leningrad (russian: links=no, translit=Blokada Leningrada, Блокада Ленинграда; german: links=no, Leningrader Blockade; ) was a prolonged military blockade undertaken by the Axis powers against the Soviet city of L ...
.
His mother, a state accountant, chose to not remarry and dedicated her life to him:
they lived on her meager salary in a 9
square meters
The square metre ( international spelling as used by the International Bureau of Weights and Measures) or square meter (American spelling) is the unit of area in the International System of Units (SI) with symbol m2. It is the area of a square ...
room in a big communal apartment, shared with other four families.
As a
secondary school
A secondary school describes an institution that provides secondary education and also usually includes the building where this takes place. Some secondary schools provide both '' secondary education, lower secondary education'' (ages 11 to 14) ...
student, he repeatedly won the city's
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
and
physics olympiads and graduated with a gold medal.
In 1955, at the age of 18, Maz'ya entered the Mathematics and Mechanics Department of Leningrad University. Taking part to the traditional mathematical olympiad of the faculty, he solved the problems for both first year and second year students and, since he did not make this a secret, the other participants did not submit their solutions causing the invalidation of the contest by the jury which therefore did not award the prize.
However, he attracted the attention of
Solomon Mikhlin
Solomon Grigor'evich Mikhlin (russian: link=no, Соломо́н Григо́рьевич Ми́хлин, real name Zalman Girshevich Mikhlin) (the family name is also transliterated as Mihlin or Michlin) (23 April 1908 – 29 August 1990) was a ...
who invited him at his home, thus starting their lifelong friendship:
and this friendship had a great influence on him, helping him develop his mathematical style more than anyone else. According to , in the years to come, "''Maz'ya was never a formal student of Mikhlin, but Mikhlin was more than a teacher for him. Maz'ya had found the topics of his dissertations by himself, while Mikhlin taught him mathematical ethics and rules of writing, referring and reviewing''".
More details on the life of Vladimir Maz'ya, from his birth to the year 1968, can be found in his autobiography .
Maz'ya graduated from Leningrad University in 1960.
[See , and .] The same year he gave two talks at
Smirnov's seminar: their contents were published as a short report in the
Proceedings of the USSR Academy of Sciences
The ''Proceedings of the USSR Academy of Sciences'' (russian: Доклады Академии Наук СССР, ''Doklady Akademii Nauk SSSR'' (''DAN SSSR''), french: Comptes Rendus de l'Académie des Sciences de l'URSS) was a Soviet journal that ...
[See .] and later evolved in his "
kandidat nauk
Candidate of Sciences (russian: кандидат наук, translit=kandidat nauk) is the first of two doctoral level scientific degrees in Russia and the Commonwealth of Independent States. It is formally classified as UNESCO's ISCED level 8, "do ...
" thesis, "''Classes of sets and embedding theorems for function spaces''",
[. See , , and : refer that "''In their reviews, the opponents and the external reviewer noted that the level of the work far exceeded the requirements of the Higher Certification Commission for Ph.D. theses, and his work was recognized as outstanding at the thesis defence in the Academic Council of Moscow State University''".] which was defended in 1962. In 1965 he earned the
Doktor nauk
Doctor of Sciences ( rus, доктор наук, p=ˈdoktər nɐˈuk, abbreviated д-р наук or д. н.; uk, доктор наук; bg, доктор на науките; be, доктар навук) is a higher doctoral degree in the Russi ...
degree, again from Leningrad University, defending the dissertation "''Dirichlet and Neumann problems in Domains with irregular boundaries''", when he was only 27. Neither the first nor his second thesis were written under the guidance of an advisor: Vladimir Maz'ya never had a formal scientific adviser, choosing the research problems he worked to by himself.
From 1960 up to 1986, he worked as a "research fellow" at the Research Institute of Mathematics and Mechanics of Leningrad University (RIMM), being promoted from junior to
senior research fellow
A research fellow is an academic research position at a university or a similar research institution, usually for Academic rank, academic staff or faculty members. A research fellow may act either as an independent investigator or under the super ...
in 1965. From 1968 to 1978 he taught at the , where he was awarded the title of "
professor
Professor (commonly abbreviated as Prof.) is an Academy, academic rank at university, universities and other post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin as a "person who pr ...
" in 1976. From 1986 to 1990 he worked to the Leningrad Section of the of the
USSR Academy of Sciences
The Academy of Sciences of the Soviet Union was the highest scientific institution of the Soviet Union from 1925 to 1991, uniting the country's leading scientists, subordinated directly to the Council of Ministers of the Soviet Union (until 1946 ...
, where he created and directed the Laboratory of Mathematical Models in Mechanics and the Consulting Center in Mathematics for Engineers.
In 1978 he married
Tatyana Shaposhnikova, a former doctoral student of Solomon Mikhlin, and they have a son, Michael: In 1990, they left the
URSS for Sweden, where Prof. Maz'ya obtained the Swedish
citizenship
Citizenship is a "relationship between an individual and a state to which the individual owes allegiance and in turn is entitled to its protection".
Each state determines the conditions under which it will recognize persons as its citizens, and ...
and started to work at Linköping University.
[See , , , and .]
Currently, he is honorary Senior Fellow of Liverpool University and
Professor Emeritus
''Emeritus'' (; female: ''emerita'') is an adjective used to designate a retired chair, professor, pastor, bishop, pope, director, president, prime minister, rabbi, emperor, or other person who has been "permitted to retain as an honorary title ...
at Linköping University: he is also member of the editorial board of several mathematical journals.
Honors
In 1962 Maz'ya was awarded the
"Young Mathematician" prize by the
Leningrad Mathematical Society
The Saint Petersburg Mathematical Society (russian: Санкт-Петербургское математическое общество) is a mathematical society run by Saint Petersburg mathematicians.
Historical notes
The St. Petersburg Mathe ...
, for his results on
Sobolev spaces
In mathematics, a Sobolev space is a vector space of functions equipped with a norm that is a combination of ''Lp''-norms of the function together with its derivatives up to a given order. The derivatives are understood in a suitable weak sense t ...
:
he was the first winner of the prize.
In 1990 he was awarded an honorary
doctorate
A doctorate (from Latin ''docere'', "to teach"), doctor's degree (from Latin ''doctor'', "teacher"), or doctoral degree is an academic degree awarded by universities and some other educational institutions, derived from the ancient formalism ''l ...
from
Rostock University
The University of Rostock (german: link=no, Universität Rostock) is a public university located in Rostock, Mecklenburg-Vorpommern, Germany. Founded in 1419, it is the third-oldest university in Germany. It is the oldest university in continen ...
.
[See , , and .] In 1999, Maz'ya received the
Humboldt Prize
The Humboldt Prize, the Humboldt-Forschungspreis in German, also known as the Humboldt Research Award, is an award given by the Alexander von Humboldt Foundation of Germany to internationally renowned scientists and scholars who work outside of G ...
.
He was elected member of the
Royal Society of Edinburgh
The Royal Society of Edinburgh is Scotland's national academy of science and letters. It is a registered charity that operates on a wholly independent and non-partisan basis and provides public benefit throughout Scotland. It was established i ...
in 2000, and of the
Swedish Academy of Science
The Royal Swedish Academy of Sciences ( sv, Kungliga Vetenskapsakademien) is one of the royal academies of Sweden. Founded on 2 June 1739, it is an independent, non-governmental scientific organization that takes special responsibility for prom ...
in 2002.
In March 2003, he, jointly with
Tatyana Shaposhnikova, was awarded the
Verdaguer Prize by the
French Academy of Sciences
The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV of France, Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific me ...
. On 31 August 2004 he was awarded the
Celsius Gold Medal, the
Royal Society of Sciences in Uppsala
The Royal Society of Sciences in Uppsala ( sv, Kungliga Vetenskaps-Societeten i Uppsala), is the oldest of the royal academies in Sweden, having been founded in 1710. The society has, by royal decree of 1906, 50 Swedish fellows and 100 foreign.
...
's top award, "''for his outstanding research on partial differential equations and hydrodynamics''". He was awarded the
Senior Whitehead Prize
The Senior Whitehead Prize of the London Mathematical Society (LMS) is now awarded in odd numbered years in memory of John Henry Constantine Whitehead, president of the LMS between 1953 and 1955. The Prize is awarded to mathematicians normally ...
by the
London Mathematical Society
The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical S ...
on 20 November 2009. In 2012 he was elected fellow of the
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
. On 30 October 2013 he was elected foreign member of the
Georgian National Academy of Sciences
The Georgian National Academy of Sciences (GNAS) ( ka, საქართველოს მეცნიერებათა ეროვნული აკადემია, tr) is a main learned society of the Georgia. It was named Georgian S ...
.
Starting from 1993, several conferences have been held to honor him: the first one, held in that year at the
University of Kyoto
, mottoeng = Freedom of academic culture
, established =
, type = Public (National)
, endowment = ¥ 316 billion (2.4 billion USD)
, faculty = 3,480 (Teaching Staff)
, administrative_staff = 3,978 (Total Staff)
, students = 22 ...
, was a conference on Sobolev spaces.
[See , and .] On the occasion of his 60th birthday in 1998, two international conferences were held in his honor: the one at the
University of Rostock
The University of Rostock (german: link=no, Universität Rostock) is a public university located in Rostock, Mecklenburg-Vorpommern, Germany. Founded in 1419, it is the third-oldest university in Germany. It is the oldest university in continen ...
was on Sobolev spaces,
while the other, at the
École Polytechnique
École may refer to:
* an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée)
* École (river), a tributary of the Seine flowing in région Île-de-France
* École, Savoi ...
in Paris,
was on the
boundary element method
The boundary element method (BEM) is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations (i.e. in ''boundary integral'' form), including fluid mechanics, acoustics, ele ...
. He was invited speaker at the
International Mathematical Congress
The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU).
The Fields Medals, the Nevanlinna Prize (to be rename ...
held in
Beijing
}
Beijing ( ; ; ), alternatively romanized as Peking ( ), is the capital of the People's Republic of China. It is the center of power and development of the country. Beijing is the world's most populous national capital city, with over 21 ...
in 2002:
his talk is an exposition on his work on Wiener–type criteria for higher order elliptic equations. Other two conferences were held on the occasion of his 70th birthday: "''Analysis, PDEs and Applications on the occasion of the 70th birthday of Vladimir Maz'ya''" was held in Rome, while the "''Nordic – Russian Symposium in honour of Vladimir Maz'ya on the occasion of his 70th birthday''" was held in Stockholm. On the same occasion, also a volume of the Proceedings of Symposia in Pure Mathematics was dedicated to him. On the occasion of his 80th birthday, a "Workshop on Sobolev Spaces and Partial Differential Equations" was held on 17–18 May 2018 was held at the
Accademia Nazionale dei Lincei
The Accademia dei Lincei (; literally the "Academy of the Lynx-Eyed", but anglicised as the Lincean Academy) is one of the oldest and most prestigious European scientific institutions, located at the Palazzo Corsini on the Via della Lungara in Rom ...
to honor him. On the 26–31 May 2019, the international conference "Harmonic Analysis and PDE" was held in his honor at the
Holon Institute of Technology
Holon Institute of Technology (HIT, he, מכון טכנולוגי חולון), is a public college in Holon, Israel. The institution focuses on science & technology, and design & visual art, and offers diverse programs that enhance the interdisc ...
.
Work
Research activity
Maz'ya authored/coauthored more than 500 publications, including 20 research monographs. Several survey articles describing his work can be found in the book , and also the paper by
Dorina and Marius Mitrea (2008) describes extensively his research achievements, so these references are the main ones in this section: in particular, the classification of the research work of Vladimir Maz'ya is the one proposed by the authors of these two references.
Theory of boundary value problems in nonsmooth domains
In one of his early papers, considers the
Dirichlet problem
In mathematics, a Dirichlet problem is the problem of finding a function which solves a specified partial differential equation (PDE) in the interior of a given region that takes prescribed values on the boundary of the region.
The Dirichlet probl ...
for the following linear elliptic equation:
:
where
* is a
bounded region
In geography, regions, otherwise referred to as zones, lands or territories, are areas that are broadly divided by physical characteristics (physical geography), human impact characteristics (human geography), and the interaction of humanity and t ...
in the –
dimensional
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordi ...
euclidean space
Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, that is, in Euclid's Elements, Euclid's ''Elements'', it was the three-dimensional space of Euclidean geometry, but in modern mathematics ther ...
* is a
matrix
Matrix most commonly refers to:
* ''The Matrix'' (franchise), an American media franchise
** ''The Matrix'', a 1999 science-fiction action film
** "The Matrix", a fictional setting, a virtual reality environment, within ''The Matrix'' (franchis ...
whose first
eigenvalue
In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted b ...
is not less than a fixed
positive
Positive is a property of positivity and may refer to:
Mathematics and science
* Positive formula, a logical formula not containing negation
* Positive number, a number that is greater than 0
* Plus sign, the sign "+" used to indicate a posit ...
constant and whose entries are
functions sufficiently smooth defined on , the
closure of .
*, and are respectively a
vector-valued function
A vector-valued function, also referred to as a vector function, is a mathematical function of one or more variables whose range is a set of multidimensional vectors or infinite-dimensional vectors. The input of a vector-valued function could ...
and two
scalar function
In mathematics and physics, a scalar field is a function associating a single number to every point in a space – possibly physical space. The scalar may either be a pure mathematical number (dimensionless) or a scalar physical quantity (wi ...
s
sufficiently smooth on as their matrix counterpart .
He proves the following
a priori estimate
In the theory of partial differential equation
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function.
The functi ...
: