Fourth-order problems with Leray-Lions type operators in variable exponent spaces

Maria-Magdalena Boureanu

doi:10.3934/dcdss.2019016

Article Contents

2019, Volume 12, Issue 2: 231-243. Doi: 10.3934/dcdss.2019016

This issue Previous Article Classical solutions for the system $\bf {\text{curl}\, v = g}$, with vanishing Dirichlet boundary conditions Next Article On the capacity approach to non-attainability of Hardy's inequality in $\mathbb{R}^N$

Fourth-order problems with Leray-Lions type operators in variable exponent spaces

Maria-Magdalena Boureanu

Department of Applied Mathematics, University of Craiova, 200585 Craiova, Rumania

Received: April 30, 2017

Revised: October 31, 2017

Published: April 2019

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Abstract

The Leray-Lions operators are versatile enough to be particularized to various elliptic operators, so they receive a lot of attention. This paper introduces to the mathematical literature Leray-Lions type operators that are appropriate for the study of the variable exponent problems of higher order. We establish some properties concerning these general operators and then we apply them to a fourth order problem with variable exponents.

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Mathematics Subject Classification: Primary: 35J40; Secondary: 35J35, 35D30, 35B38.

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