Existence and uniqueness of entropy solutions to nonlinear elliptic problems with variable growth

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Résumé

The authors study the boundary value problem
{u−div(a(x,∇u))=fu=0inΩ,onΩ,
where Ω is a smooth bounded domain in RN(N≥3) and div(a(x,∇u)) is a p(x)-Laplace type operator. The main results presented are Theorems 3.2 and 4.3, obtained by using variational arguments, which establish the existence and uniqueness of weak energy solutions, for f∈L∞(Ω), and entropy solutions, for f∈L1(Ω), to the above problem.
There are a few misprints in this article.

Mots-clés

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