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Remarks on Gårding inequalities for differential operators

Xavier Saint Raymond — 2002

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Classical Gårding inequalities such as those of Hörmander, Hörmander-Melin or Fefferman-Phong are proved by pseudo-differential methods which do not allow to keep a good control on the supports of the functions under study nor on the smoothness of the coefficients of the operator. In this paper, we show by very simple calculations that in certain special situations, the results that can be obtained directly are much better than those expected thanks to the general theory.

Unicité de Cauchy à partir de surfaces faiblement pseudo-convexes

Xavier Saint Raymond — 1989

Annales de l'institut Fourier

Le théorème d’unicité classique de Hörmander affirme qu’il y a prolongement unique des solutions d’équations principalement normales à travers les surfaces fortement pseudo-convexes. Le cas des surfaces faiblement pseudo-convexes est envisagé ici avec des hypothèses de transversalité aux points où le terme de pseudo-convexité s’annule (type biprinicipal). Pour ces situations, deux résultats sont donnés : un résultat d’unicité compacte démontré par la technique des inégalités de Carleman, et un résultat...

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