Existence and uniqueness for nonlinear anisotropic elliptic equations

Abstract

We study the existence and uniqueness for weak solutions to some classes of anisotropic elliptic Dirichlet problems with data belonging to the natural dual space

A Symmetrization Result for a Class of Anisotropic Elliptic Problems

“…In the last years anisotropic problems have been extensively studied by many authors (see e.g. [AdBF2,AdBF3,ACh,BMS,DFG,DF,FGK,FGL,FS,G,Mar]).…”

Existence Results for Nonlinear Anisotropic Elliptic Equation

“…In this work, we prove the existence of weak solu-* Corresponding Author: Youssef Akdim, FP , Taza, Morocco & youssef.akdim@usmba.ac.ma tions of the problem (1), based on techniques related to that of Di castro in [11] and to the recent work's Di Nardo and F. Feo in [9].…”

“…In [5], F. Li has proved the existence and regularity of weak solutions of the problem (1) with g i = 0, H i = 0, k i = 0 for all i = 1, ..., N and f belongs to L m (Ω) with m > 1. In [9], R. Di Nardo and F. Feo have proved the existence of weak solution of the problem (1) when g i = 0 for all i = 1, ..., N . In [10], we have proved the existence and uniqueness of weak solution of the problem (1) but when…”

Existence of entropy solutions for some nonlinear elliptic problems involving variable exponent and measure data

“…they proved the existence of renormalized solutions and some regularity results, (see also. [6,12,16]). Aharouch and Bennouna [3] have studied the quasilinear unilateral problems of the type:…”