descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jan 1969Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 20, page 24 (issn: 0002-9939,

Authors: Robert A. Adams;

doi: 10.2307/2035953 , 10.1090/s0002-9939-1969-0243191-0

Ellipticity and Regularity for Periodic Nonlinear Equations

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Abstract

The composition of two strongly elliptic linear operators with suitably differentiable coefficients is also strongly elliptic. This fact has been used [3, pp. 178-181] to yield a particularly simple proof of the regularity of weak solutions of periodic strongly elliptic linear equations. In this paper we prove a similar regularity theorem for periodic nonlinear equations under the assumption of strong ellipticity for the composition of the given nonlinear operator with certain linear operators. Let A be a nonlinear differential operator of order 2m given by

Keywords

partial differential equations

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