Existence of a renormalized solution for some nonlinear anisotropic elliptic problems
Youssef Akdim, Mohammed El Ansari, Soumia Lalaoui Rhali · Gulf Journal of Mathematics · 2018
In this paper, we study a general class of nonlinear anisotrpic elliptic problems associated with the differential inclusion β(u) - div(a(x, D(u) + F(u)) ∋ f in Ω, where f ∈ L∞(Ω). A vector field a(. , .) is a Caratheodory function. Using trunction techniques and the generalized monotonicity method in the functional spaces we prove the existence of renormalized solutions for L∞-data.