BOUNDARY PROBLEMS FOR FRACTIONAL LAPLACIANS

Author:

GUAN QING-YANG1,MA ZHI-MING1

Affiliation:

1. Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China

Abstract

By making use of the reflected α-stable process on a closed domain of ℝn 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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Modelling and Simulation

Reference36 articles.

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