Uniqueness  for elliptic  problems with   Hölder--type dependence on the solution

Lucio Boccardo; Alessio Porretta

doi:10.3934/cpaa.2013.12.1569

Article Contents

2013, Volume 12, Issue 4: 1569-1585. Doi: 10.3934/cpaa.2013.12.1569

This issue Previous Article Keller-Osserman estimates for some quasilinear elliptic systems Next Article On Dirichlet, Poncelet and Abel problems

Uniqueness for elliptic problems with Hölder--type dependence on the solution

Lucio Boccardo^1, and
Alessio Porretta^2,

1.
Dipartimento di Matematica, Università di Roma 1, Piazza A. Moro 2, 00185 Roma
2.
Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientica 1, 00133 Roma

Received: May 2011

Revised: June 2012

Published: July 2013

Abstract / Introduction Related Papers Cited by

Abstract

We prove uniqueness of weak (or entropy) solutions for nonmonotone elliptic equations of the type \begin{eqnarray} -div (a(x,u)\nabla u)=f \end{eqnarray} in a bounded set $\Omega\subset R^N$ with Dirichlet boundary conditions. The novelty of our results consists in the possibility to deal with cases when $a(x,u)$ is only Hölder continuous with respect to $u$.

Keywords:

Mathematics Subject Classification: Primary: 35J60; Secondary: 35J65.

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