Guido Stampacchia (26 March 1922 – 27 April 1978) was an Italian

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 ...

, known for his work on the theory of

variational inequalities In mathematics, a variational inequality is an inequality involving a functional, which has to be solved for all possible values of a given variable, belonging usually to a convex set. The mathematical theory of variational inequalities was initi ...

, the

calculus of variation The calculus of variations (or Variational Calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions t ...

and the theory of

elliptic partial differential equation Second-order linear partial differential equations (PDEs) are classified as either elliptic, hyperbolic, or parabolic. Any second-order linear PDE in two variables can be written in the form :Au_ + 2Bu_ + Cu_ + Du_x + Eu_y + Fu +G= 0,\, wher ...

s..

Life and academic career

Stampacchia was born in

Naples Naples (; it, Napoli ; nap, Napule ), from grc, Νεάπολις, Neápolis, lit=new city. is the regional capital of Campania and the third-largest city of Italy, after Rome and Milan, with a population of 909,048 within the city's adminis ...

, Italy, to Emanuele Stampacchia and Giulia Campagnano. He obtained his high school certification from the Liceo-Ginnasio

Giambattista Vico Giambattista Vico (born Giovan Battista Vico ; ; 23 June 1668 – 23 January 1744) was an Italian philosopher, rhetorician, historian, and jurist during the Italian Enlightenment. He criticized the expansion and development of modern rationali ...

in Naples in classical subjects, although he showed stronger aptitude for

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 Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

. In 1940 he was admitted to the

Scuola Normale Superiore di Pisa The Scuola Normale Superiore in Pisa (commonly known in Italy as "la Normale") is a public university in Pisa and Florence, Tuscany, Italy, currently attended by about 600 undergraduate and postgraduate (PhD) students. It was founded in 1810 wi ...

for undergraduate studies in

pure mathematics Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may originate in real-world concerns, and the results obtained may later turn out to be useful for practical applications, ...

. He was drafted in March 1943 but nevertheless managed to take examinations during the summer before joining the resistance movement against the Germans in the defense of Rome in September. He was discharged in June 1945. In 1944 he won a scholarship to the

University of Naples The University of Naples Federico II ( it, Università degli Studi di Napoli Federico II) is a public university in Naples, Italy. Founded in 1224, it is the oldest public non-sectarian university in the world, and is now organized into 26 depar ...

which allowed him to continue his studies. In the 1945–1946 academic year he declined a specialization at the Scuola Normale in the Faculty of Sciences in favour of an assistant position at the Istituto Universitario Navale. In 1949 he was appointed as assistant with tenure to the chair of mathematical analysis, and in 1951 he obtained his "Libera docenza". In 1952 won a national competition for the chair at the

University of Palermo The University of Palermo ( it, Università degli Studi di Palermo) is a university located in Palermo, Italy, and founded in 1806. It is organized in 12 Faculties. History The University of Palermo was officially founded in 1806, although its ...

. He was nominated Professor on Probation at the

University of Genoa The University of Genoa, known also with the acronym UniGe ( it, Università di Genova), is one of the largest universities in Italy. It is located in the city of Genoa and regional Metropolitan City of Genoa, on the Italian Riviera in the Liguri ...

later the same year and was promoted to full Professor in 1955. He married fellow student Sara Naldini in October 1948. Children Mauro, Renata, Giulia, and Franca were born in 1949, 1951, 1955 and 1956 respectively. Stampacchia was active in research and teaching throughout his career. He made key contributions to a number of fields, including

and

differential equations In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...

. In 1967 Stampacchia was elected President of the

Unione Matematica Italiana The Italian Mathematical Union ( it, Unione Matematica Italiana) is a mathematical society based in Italy. It was founded on December 7, 1922 by Luigi Bianchi, Vito Volterra, and most notably, Salvatore Pincherle, who became the Union's first P ...

. It was about this time that his research efforts shifted toward the emerging field of

, which he modeled after

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 for

partial differential equations In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to ...

. He was also director of the

Istituto per le Applicazioni del Calcolo The Istituto per le Applicazioni del Calcolo Mauro Picone ( en, Institute for Calculus Applications "Mauro Picone"), abbreviated IAC, is an applied mathematics institute, part of the Consiglio Nazionale delle Ricerche. It was founded in 1927 as a p ...

Consiglio Nazionale delle Ricerche The National Research Council (Italian: ''Consiglio Nazionale delle Ricerche, CNR'') is the largest research council in Italy. As a public organisation, its remit is to support scientific and technological research. Its headquarters are in Rome. ...

from December 1968Silvia Mazzone,
Guido Stampacchia
'' to 1974. Stampacchia accepted the position of Professor Mathematical Analysis at the University of Rome in 1968 and returned to the University of Pise in 1970 and subsequently with the chair of Higher Analysis at the Scuola Normale Superiore. In early 1978 he suffered a serious heart attack and died of heart arrest on 27 April that year while he was in Paris as Visiting Professor. The Stampacchia Medal, an international prize awarded every three years for contributions to the

Calculus of Variations The calculus of variations (or Variational Calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions t ...

, was established in 2003.

Selected works

*. *with

Sergio Campanato Sergio Campanato (17 February 1930 – 1 March 2005) was an Italian mathematician who studied the theory of regularity for elliptic and parabolic partial differential equations. Career He graduated in mathematics and physics at the Universit ...

, ''Sulle maggiorazioni in L^p nella teoria delle equazioni ellittiche'', Bollettino dell’Unione Matematica Italiana, Bologna, Zanichelli, 1965. * with Jaurès Cecconi, ''Lezioni di analisi matematica, I: Funzioni di una variabile'', Napoli: Liguori editore, 1974, * with Jaurès Cecconi, ''Lezioni di analisi matematica, II: Funzioni di più variabili'', Napoli: Liguori, 1980, * with Jaurès Cecconi and Livio Clemente Piccinini, ''Esercizi e problemi di analisi matematica'', Napoli: Liguori, 1996, , *, translated in English as . *with David Kinderlehrer
''An introduction to variational inequalities and their applications''
NY, Academic Press, 1980 ** Reprint:

Society for Industrial and Applied Mathematics Society for Industrial and Applied Mathematics (SIAM) is a professional society dedicated to applied mathematics, computational science, and data science through research, publications, and community. SIAM is the world's largest scientific socie ...

, 2000 ()

Notes

References

Biographical references

*. The chapter on Stampacchia in the a book collecting brief biographical sketches and bibliographies of the scientific the work produced by the mathematicians who worked at the

Parthenope University of Naples The Parthenope University of Naples ( it, Università degli Studi di Napoli "Parthenope") is one of the universities located in Naples, Italy. Historical notes Now one of the fully accredited universities of Naples, the “Parthenope” Universi ...

during their stay. *. The biographical and bibliographical entry (updated up to 1976) on Guido Stampacchia, published under the auspices of the Accademia dei Lincei in a book collecting many profiles of its living members up to 1976.

General references

External links

* * {{DEFAULTSORT:Stampacchia, Guido 20th-century Italian mathematicians Mathematical analysts PDE theorists Variational analysts Members of the Lincean Academy 1922 births 1978 deaths Scientists from Naples University of Pisa alumni Scuola Normale Superiore di Pisa alumni Academic staff of the University of Pisa National Research Council (Italy) people Presidents of the Italian Mathematical Union