Nonlinear multivalued problems with variable exponent and diffuse measure data in anisotropic space

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Résumé

We study a nonlinear elliptic problem governed by a general anisotropic operator with variable exponents and Radon diffuse measure data. We start by proving the existence of a renormalized solution and we establish that the notion of renormalized solution is equivalent to the notion of entropy solution. Finally, we show the uniqueness of the entropy solution

Mots-clés

nonlinear elliptic equation; renormalized solution; entropy solution