BOUNDARY PROBLEMS FOR FRACTIONAL LAPLACIANS-Reference-Cited by-同舟云学术

BOUNDARY PROBLEMS FOR FRACTIONAL LAPLACIANS

Published:2005-09 Issue:03 Volume:05 Page:385-424
ISSN:0219-4937
Container-title:Stochastics and Dynamics
language:en
Short-container-title:Stoch. Dyn.

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

Link

https://www.worldscientific.com/doi/pdf/10.1142/S021949370500150X

Reference36 articles.

1. Lévy Processes and Stochastic Calculus

2. Universitext;Bliedtner J.,1996

3. Censored stable processes

Cited by 80 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. An adaptive non-uniform L2 discretization for the one-dimensional space-fractional Gray–Scott system;Communications in Nonlinear Science and Numerical Simulation;2024-11

2. Dynamic boundary conditions for time dependent fractional operators on extension domains;Advances in Differential Equations;2024-09-01

3. Multiplicity of Normalized Solutions to a Fractional Logarithmic Schrödinger Equation;Fractal and Fractional;2024-06-29

4. Existence of periodic measures of fractional stochastic delay complex Ginzburg-Landau equations on Rn;Journal of Mathematical Physics;2024-06-01

5. Multiplicity of Normalized Solutions for the Fractional Schrödinger Equation with Potentials;Mathematics;2024-03-05