Weak and entropy solutions to nonlinear elliptic problems with variable exponent.

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Résumé

The authors study nonlinear boundary value problem with the nonlinear operator of p-Laplacian-type and Dirichlet boundary condition. The authors obtain two existence results: in first a unique entropy solution is obtain and in the second a week solution is produced.

Mots-clés

generalized Lebesgue-Sobolev spaces; weak energy solution; entropy solution; p(x)-Laplace operator; electrorheological fluids