ON CLASS OF FRACTIONAL ELLIPTIC PROBLEMS

Abstract

The work presented in this dissertation is devoted to study a class of fractional elliptic problems involving the fractional Laplacian operator (−∆) s for s ∈ (0, 1).We recall the essential definitions and notions which we will use in the later chapters.Then,we prove the existence of the unique solution by variational method, and We’ll also prove some regularity estimate for the fractional laplacian problems .Finly, we using the Mountain Pass Theorem to prove the existence of solutions for equations driven by a non-local integro-differential operator with homogeneous Dirichlet boundary conditions.