Solution of Laplace’s Equation in A Singular Domain Using Mellin Transform

Abstract

This paper deals with the theory of V. Kondratiev which allows to study the regularity of elliptical problems in corner domains. After having introduced the Mellin transform and the Sobolev spaces to weight, we recall the links with Sobolev spaces. The Mellin transform represent an important key to study the H^s regularity in corner domains.