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

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  • 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 $u$.
    Mathematics Subject Classification: Primary: 35J60; Secondary: 35J65.


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