A variational approach to a class of quasilinear elliptic equations not in divergence form

M. Matzeu; Raffaella Servadei

doi:10.3934/dcdss.2012.5.819

Article Contents

2012, Volume 5, Issue 4: 819-830. Doi: 10.3934/dcdss.2012.5.819

This issue Previous Article On the existence of nontrivial solutions of inequalities in Orlicz-Sobolev spaces Next Article Three solutions with precise sign properties for systems of quasilinear elliptic equations

A variational approach to a class of quasilinear elliptic equations not in divergence form

M. Matzeu^1, and
Raffaella Servadei^2,

1.
Dip. di Matematica, Università di Roma "Tor Vergata", Via della Ricerca Scientifica - 00133 - Roma
2.
Dipartimento di Matematica, Università della Calabria, Ponte Pietro Bucci 31 B, Arcavacata di Rende (Cosenza), 87036

Received: January 31, 2011

Revised: April 30, 2011

Published: July 2012

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Abstract

The aim of this paper is to use a variational approach in order to obtain the existence of non-trivial weak solutions of a quasilinear elliptic equation not in divergence form, in dimension $N=3$. Moreover, we prove that our solution is $C^{1, \alpha}(\overline\Omega)$ and also locally $C^{2, \alpha}(\overline\Omega)$ for a suitable $\alpha\in (0,1)$.

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Mathematics Subject Classification: Primary: 35J20, 35J65; Secondary: 35J25.

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