Vol. 1, No. 3, 2019

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

Makhlouf Derridj

Vol. 1 (2019), No. 3, 321–345
Abstract

Given a general Hörmander’s operator P = j=1mXj2 + Y + b in an open set Ω n, where Y,X1,,Xm are smooth real vector fields in Ω, b C(Ω), and given also an open, relatively compact set Ω0 with Ω¯0 Ω, and s , s 1, such that the coefficients of P are in Gs(Ω0) and P satisfies a 1 p-Sobolev estimate in Ω0, our aim is to establish local estimates reflecting local domination of ordinary derivatives by powers of P, in Ω0. As an application, we give a direct proof of the G2ps(Ω0)-regularity of any Gs(Ω0)-vector of P.

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Keywords
Gevrey vectors, Degenerate elliptic-parabolic differential operators.
Mathematical Subject Classification 2010
Primary: 35B65, 35G99, 35J70, 35K65
Milestones
Received: 24 November 2017
Revised: 11 December 2017
Accepted: 31 May 2018
Published: 8 August 2018
Authors
Makhlouf Derridj
78350 Les Loges en Josas
France