Sous-ellipticité d’opérateurs intégro-différentiels vérifiant le principe du maximum. (Subellipticity of integro-differential operators satisfying the maximum principle). (French) Zbl 0742.35077

Cancelier, C. E.; Chemin, J. Y.

Sémin. Équ. Dériv. Partielles, Éc. Polytech., Cent. Math., Palaiseau 1990-1991, No.XXII, 10 p. (1991).

Summary: In this paper, we prove the ellipticity of pseudodifferential operators with non integer order and positive kernels not vanishing too much, and the subellipticity of operators \(P=\sum_ jX^*_ jX_ j\) of order \(\leq 2\) when there exists an elliptic commutator of the pseudodifferential operators \(X_ j\).

MSC:

35S05	Pseudodifferential operators as generalizations of partial differential operators
47G30	Pseudodifferential operators
35B50	Maximum principles in context of PDEs

Keywords:

ellipticity; subellipticity