BOUNDARY PROBLEMS FOR FRACTIONAL LAPLACIANS

Abstract

By making use of the reflected α-stable process on a closed domain of ℝ n and its killed subprocess on part of the domain, in this paper we study the boundary value problem for the Schrödinger type equation of a fractional Laplacian. The boundary condition is imposed partly follow Dirichlet condition and partly follow Neuman condition. We obtain the existence and the uniqueness resutls. The solution is expressed as a functional of the reflected α-stable process.