Semilinear equations for non-local operators: beyond the fractional Laplacian

TL;DR

This paper investigates semilinear equations involving a broad class of non-local operators, extending beyond the fractional Laplacian, and provides results for solutions in bounded domains with various boundary conditions.

Contribution

It introduces new analytical results for semilinear non-local operators in general and smooth bounded domains, surpassing the fractional Laplacian case.

Findings

Existence and uniqueness results for solutions in bounded domains.

Extension of results to general non-local operators beyond fractional Laplacian.

Analysis in $C^{1,1}$ domains for boundary value problems.

Abstract

We study semilinear problems in general bounded open sets for non-local operators with exterior and boundary conditions. The operators are more general than the fractional Laplacian. We also give results in case of bounded $C^{1,1}$ open sets.