Existence of solutions for nonlinear degenerate elliptic equations with L^{m}-data and Neumann boundary condition

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Résumé

In this paper, we consider the following homogenous Neumann elliptic problem
 
=f in Ω, on ∂Ω,
−div 
(2)
NN
 XX 
 − Di(a(x,u,∇u))+ i
i=1    XN
solutions in the sense of distributions for our elliptic problem in the anisotropic Sobolev spaces.

Mots-clés

Anisotropic Sobolev spaces, Neumann boundary condition, nonlinear elliptic problem, solutions in the sense of distributions