Regularity and weak comparison principles for double phase quasilinear elliptic equations

Giuseppe Riey

doi:10.3934/dcds.2019198

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2019, Volume 39, Issue 8: 4863-4873. Doi: 10.3934/dcds.2019198

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Regularity and weak comparison principles for double phase quasilinear elliptic equations

Giuseppe Riey

Dipartimento di Matematica e Informatica, Università della Calabria, Via P. Bucci, 87036 Rende (CS), Italy

Received: October 31, 2018

Revised: January 31, 2019

Published: May 2019

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Abstract

We consider the Euler equation of functionals involving a term of the form

$ \int_{\Omega}(| \nabla u|^p+a(x)| \nabla u|^q) \,{ {\rm{d}}} x, $

with $ 1<p<q<p+1 $ and $ a(x)\geq 0 $. We prove weak comparison principle and summability results for the second derivatives of solutions.

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Mathematics Subject Classification: Primary: 35B05, 35B65, 35J92; Secondary: 35D10.

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