Renormalized solutions for a p(·)-Laplacian equation with Neumann nonhomogeneous boundary condition involving diffuse measure data and variable exponent

Abstract

In this paper we prove the existence of at least one renormalized solution for the p(x)-Laplacian equation associated with a maximal monotone operator and Radon measure data. The functional setting involves Sobolev spaces with variable exponent W 1, p (·)(W).

Existence and stability of solutions to nonlinear parabolic problems with perturbed gradient and measure data

“…Therefore, the study of problems related to problem (P ) are also of interest, since these problems is a very active field (see [8][9][10][11][12]). In these papers, the authors consider on the one hand a Leray-Lions type operator, which permit them to exploit the growth condition, the coerciveness condition and the monotonicity condition of the operator and the other hand in these papers the boundaries conditions are homogeneous Dirichlet type, which allows them to exploit a result of decomposition of diffuse Radon measure which is suitable for this type of situation (cf.…”