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... > equation > functional equation > differential equation > partial differential equation > hypoelliptic operator

... > calculus > differential calculus > differential equation > partial differential equation > hypoelliptic operator

mathematical physics > differential operator > hypoelliptic operator

mathematical analysis > functional analysis > operator > differential operator > hypoelliptic operator

Preferred term

hypoelliptic operator

Definition(s)

In the theory of partial differential equations, a partial differential operator ${\\displaystyle P}$ defined on an open subset

${\\displaystyle U\\subset {\\mathbb {R} }^{n}}$

is called hypoelliptic if for every distribution ${\\displaystyle u}$ defined on an open subset ${\\displaystyle V\\subset U}$ such that ${\\displaystyle Pu}$ is ${\\displaystyle C^{\\infty }}$ (smooth), ${\\displaystyle u}$ must also be ${\\displaystyle C^{\\infty }}$ .

(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Hypoelliptic_operator)

Broader concept(s)

In other languages

opérateur hypoelliptique

French

URI

http://data.loterre.fr/ark:/67375/PSR-WL1Z5XG9-5

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