Uniqueness for elliptic problems with Hölder--type dependence on the solution
Lucio Boccardo, Alessio Porretta · Communications on Pure & Applied Analysis · 2012
We prove uniqueness of weak (or entropy) solutions for nonmonotone elliptic equations of the type\begin{eqnarray}-div (a(x,u) abla 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 $u$.