We prove uniqueness of weak (or entropy) solutions for nonmonotone elliptic equations of the type -div(a (x, u)del u) = f in a bounded set Omega subset of 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 Holder continuous with respect to u.
Uniqueness for elliptic problems with hölder-type dependence on the solution / Boccardo, Lucio; Alessio, Porretta. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - STAMPA. - 12:4(2013), pp. 1569-1585. [10.3934/cpaa.2013.12.1569]
Uniqueness for elliptic problems with hölder-type dependence on the solution
BOCCARDO, Lucio;
2013
Abstract
We prove uniqueness of weak (or entropy) solutions for nonmonotone elliptic equations of the type -div(a (x, u)del u) = f in a bounded set Omega subset of 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 Holder continuous with respect to u.File allegati a questo prodotto
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