Vol. 302, No. 2, 2019

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Local estimates for Hörmander's operators of first kind with analytic Gevrey coefficients and application to the regularity of their Gevrey vectors

Makhlouf Derridj

Vol. 302 (2019), No. 2, 511–543
Abstract

Following our preceding papers devoted to the case of general Hörmander’s operators P with analytic-Gevrey coefficients on an open set Ω in n, for which we established local relations of domination by powers of P and derived from it local s-Gevrey regularity of local s-Gevrey vectors of P (with, furthermore, suitable relations between s,s and the coefficient of the Sobolev estimate satisfied by P), this article deals with the case of Hörmander’s operators of first kind (or of degenerate elliptic kind). We establish, in this case, precise local relations of domination by powers of P which give, when applied to the s-Gevrey regularity of s-Gevrey vectors of P, in Ω0, with Omega¯0 Ω, an optimal relation between s,s and the type of Omega¯0 with respect to the system X of vector fields whose sum of squares is the leading part of P.

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Keywords
Gevrey vectors, degenerate elliptic-parabolic differential operators
Mathematical Subject Classification 2010
Primary: 35B65, 35J70
Secondary: 35G99
Milestones
Received: 3 September 2018
Revised: 6 September 2018
Accepted: 18 February 2019
Published: 27 November 2019
Authors
Makhlouf Derridj
(Personal address)
5 rue de la Juviniere
78350 Les Loges-en-Josas
France