Semilinear Dirichlet problem for subordinate spectral Laplacian

Abstract

We study semilinear problems in bounded $C^{1,1}$ domains for non-local operators with a boundary condition. The operators cover and extend the case of the spectral fractional Laplacian. We also study harmonic functions with respect to the non-local operator and boundary behaviour of Green and Poisson potentials.

arXiv comment54 pages, some typos correted, to appear in Communications on Pure and Applied Analysis