p(.)-Elliptic inclusion problem with natural growth term and Fourie type Boundary condition

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Résumé

In this paper, we discuss the existence of renormalized and entropy solutions of nonlinear elliptic problems governed by the general p(.)-Leray-Lions type operator with a natural growth term subject to L1 data in the interior of the domain and Fourier type condition on the boundary. We first introduce a sequence of approximated prob- lems by regularizing the data via truncation and Yosida’s method. Then, using the technique of maximal monotone operators in Banach spaces, we prove that the ap- proximated problem is well-posed in terms of a weak solution. Finally, we pass to the limit and prove that the sequence of approximated solutions converges to the entropy or renormalized solutions of the initial given problem

Mots-clés

Nonlinear Elliptic Problems, Partial Differential Equations, Weak Solutions