Existence of Renormalized Solutions for Some Anisotropic Quasilinear Elliptic Equations

T. Ahmedatt, A. Ahmed, H. Hjiaj, A. Touzani

In this paper, we consider a class of anisotropic quasilinear elliptic equations of the type $$eft\{\begin{array}{ll} \displaystyle- um_{i=1}^{N} tial^{i}a_{i}(x,u,abla u) + |u|^{s(x)-1}u = f(x,u), & \mbox{in } mega, u = 0& ext{on } tialmega, \end{array} \right.$$ where $f(x,s)$ is a Carathéodory function which satisfies some growth condition. We prove the existence of renormalized solutions for our Dirichlet problem, and some regularity results are concluded.