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2019 Local estimates for Hörmander's operators with Gevrey coefficients and application to the regularity of their Gevrey vectors
Makhlouf Derridj
Tunisian J. Math. 1(3): 321-345 (2019). DOI: 10.2140/tunis.2019.1.321

Abstract

Given a general Hörmander’s operator P = j = 1 m X j 2 + Y + b in an open set Ω n , where Y , X 1 , , X m are smooth real vector fields in Ω , b C ( Ω ) , and given also an open, relatively compact set Ω 0 with Ω ¯ 0 Ω , and s , s 1 , such that the coefficients of P are in G s ( Ω 0 ) and P satisfies a 1 p -Sobolev estimate in Ω 0 , our aim is to establish local estimates reflecting local domination of ordinary derivatives by powers of P , in Ω 0 . As an application, we give a direct proof of the G 2 p s ( Ω 0 ) -regularity of any G s ( Ω 0 ) -vector of P .

Citation

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Makhlouf Derridj. "Local estimates for Hörmander's operators with Gevrey coefficients and application to the regularity of their Gevrey vectors." Tunisian J. Math. 1 (3) 321 - 345, 2019. https://doi.org/10.2140/tunis.2019.1.321

Information

Received: 24 November 2017; Revised: 11 December 2017; Accepted: 31 May 2018; Published: 2019
First available in Project Euclid: 15 December 2018

zbMATH: 07027458
MathSciNet: MR3907743
Digital Object Identifier: 10.2140/tunis.2019.1.321

Subjects:
Primary: 35B65, 35G99, 35J70, 35K65

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.1 • No. 3 • 2019
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