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Hypoelliptic operator

In the theory of partial differential equations, a partial differential operatorP{\displaystyle P} defined on an open subsetU⊂Rn{\displaystyle U\subset {\mathbb {R} }^{n}}is called hypoelliptic if for every distributionu{\displaystyle u} defined on an open subset V⊂U{\displaystyle V\subset U} such that Pu{\displaystyle Pu} is C∞{\displaystyle C^{\infty }} (smooth), u{\displaystyle u} must also be C∞{\displaystyle C^{\infty }}.

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