Multivalued anisotropic problem with Neumann boundary condition involving diffuse Radon measure data and variable exponent

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Résumé

We study a nonlinear anisotropic elliptic problem with homogeneous Neumann boundary condition governed by a general anisotropic operator with variable exponents and diffuse Radon measure data that is the Radon measure which does not charge the sets of zero p(⋅)-capacity. We firstly prove the existence of renormalized solutions. Secondly, we show an equivalence between renormalized solution and entropy solution. Thirdly, we end by proving an uniqueness result of entropy solution

Mots-clés

Neumann boundary; anisotropic Sobolev spaces; renormalized solution; entropy solution; maximal monotone graph; Radon diffuse measure; Marcinkiewicz spaces; p(⋅)-capacity