Regularity Theorems for Elliptic and Hypoelliptic Operators Via the Global Relation

Regularity Theorems for Elliptic and Hypoelliptic Operators Via the Global Relation

Year:    2011

Journal of Partial Differential Equations, Vol. 24 (2011), Iss. 1 : pp. 83–96

Abstract

In this paperwe give a newproof regarding the regularity of solutions to hypoelliptic partial differential equations with constant coefficients. On the assumption of existence, we provide a spectral representation for the solution and use this spectral representation to deduce regularity results. By exploiting analyticity properties of the terms within the spectral representation, we are able to give simple estimates for the size of the derivatives of the solutions and interpret them in terms of Gevrey classes.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jpde.v24.n1.6

Journal of Partial Differential Equations, Vol. 24 (2011), Iss. 1 : pp. 83–96

Published online:    2011-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    14

Keywords:    Hypoelliptic operators

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