Existence and uniqueness of a renormalized solution of a multivalued Fourier problem with L¹-data

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Résumé

In this manuscript, we are concerned with the existence and uniqueness of the renormalized solution of a nonlinear elliptic problem β (u)−div a(x, Du) ∋ f in Ω, coupled with a Fourier boundary conditions a(x, Du). η + λu = g on ∂Ω, where f and g are functions of L 1 (Ω) and L 1 (∂Ω) respectively. The functional setting involves Lebesgue and Sobolev spaces with variable exponent. Some a-priori estimates are used to obtain our results.

Mots-clés

Renormalized solution, Nonlinear elliptic problem, Fourier boundary conditions, Existence and uniqueness.