Isotropic problem with non homogeneous Dirichlet boundary condition and L1-data

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Résumé

The purpose of this paper is to study an isotropic problem with non homogeneous Dirichlet
boundary condition and L1-data in a variable-exponent Sobolev space. We start by showing
the existence and uniqueness of the weak solution when the source term is bounded. Finally,
we use a problem-based approach to prove the existence and uniqueness of entropy solution
when the source term is integrable.

Mots-clés

Sobolev spaces, variable exponent, weak solution, entropy solution