ON SOME FRACTIONAL p -LAPLACIAN PROBLEMS

Abstract

In this dissertation, we study some fractional elliptic equations. We begin by presenting some facts about the fractional Sobolev spaces and we introduce some definitions and some properties of the fractional Laplacian operator. Then, we prove the existence and the uniqueness of solution of Laplace fractional equation using two methods; Lax-Milgram theorem and Variational Method. We end this work by applying Minty-Browder method to establish the existence and the uniqueness of the weak solution for the p -Laplacian fractional equation.