Vol. 1, No. 3, 2019

Download this article
Download this article For screen
For printing
Recent Issues
Volume 6, Issue 1
Volume 5, Issue 4
Volume 5, Issue 3
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the journal
Ethics and policies
Peer-review process
Statement, 2023
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 2576-7666
ISSN (print): 2576-7658
Author index
To appear
 
Other MSP Journals
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.

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