NEUMANN PROBLEMS FOR NONLINEAR ELLIPTIC EQUATIONS INVOLVING VARIABLE EXPONENT AND MEASURE DATA

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Résumé

This paper deals with the question of the existence of entropy solutions for the problem −div(a(x,u,∇u)+ϕ(u))+g(x,u,∇u)=μ posed in an open bounded subset Ω of ℝN with the homogeneous Neumann boundary condition (a(x,u,∇u)+ϕ(u))⋅η=0. The functional setting involves Lebesgue and Sobolev spaces with variable exponent

Mots-clés

quasilinear elliptic equation; Neumann condition; existence of entropy solutions