Boundary integral operator for the fractional Laplace equation in a bounded Lipschitz domain

TL;DR

This paper investigates the boundary integral operator associated with the fractional Laplace equation in bounded Lipschitz domains and applies it to boundary value problems involving fractional Laplacians.

Contribution

It introduces a boundary integral operator framework for fractional Laplace equations in Lipschitz domains, advancing boundary integral methods for nonlocal operators.

Findings

Characterization of the boundary integral operator for fractional Laplace equations.

Application of the operator to solve boundary value problems.

Insights into the properties of solutions in Lipschitz domains.

Abstract

We study the boundary integral operator induced from fractional Laplace equation in a bounded Lipschitz domain. As an application, we study the boundary value problem of a fractional Laplace equation.