BOUNDARY INTEGRAL OPERATOR FOR THE FRACTIONAL LAPLACIAN ON THE BOUNDARY OF A BOUNDED SMOOTH DOMAIN

摘要

We introduce the boundary integral operator induced from the fractional Laplace equation on the boundary of a bounded smooth domain. For 1/2 < alpha < 1, we show the bijectivity of the boundary integral operator S-2 alpha : L-p(partial derivative Omega) -> H-p(2 alpha-1) (partial derivative Omega) for 1 < p < infinity. As an application, we demonstrate the existence of the solution of the Dirichlet boundary value problem of the fractional Laplace equation.