Mohamed Badr Benboubker, Stanislas Ouaro, Urbain Traore

Neumann Problems for Nonlinear Elliptic Equations Involving Variable Exponent and Measure Data

abstract:
This paper deals with the question of the existence of entropy solutions for the problem $ -\ddiv(a(x, u, \nabla u) + \phi(u))+g(x,u,\nabla u)= \mu $ posed in an open bounded subset $\Omega$ of $\mathbb{R}^{N}$ with the homogeneous Neumann boundary condition $(a(x, u, \nabla u) + \phi(u))\cdot\eta =0$. The functional setting involves Lebesgue and Sobolev spaces with variable exponent.

Mathematics Subject Classification: 35J25, 35J60, 35Dxx

Key words and phrases: Nonlinear elliptic problem, variable exponents, entropy solution, Neumann boundary conditions, Radon measure