Large solutions to semilinear equations for subordinate Laplacians in $C^{1,1}$ bounded open sets

TL;DR

This paper investigates the existence of large solutions to semilinear equations involving subordinate Laplacians, a class of nonlocal operators generalizing the fractional Laplacian, in bounded $C^{1,1}$ domains.

Contribution

It establishes existence results for large solutions under a nonlocal Keller-Osserman condition for a broad class of subordinate Laplacians.

Findings

Existence of large solutions in bounded $C^{1,1}$ sets.

Extension of Keller-Osserman condition to nonlocal operators.

Generalization of fractional Laplacian results to subordinate Laplacians.

Abstract

We study the existence of a large solution to a semilinear problem in a bounded open $C^{1,1}$ set for a class of nonlocal operators obtained by an appropriate subordination of the Laplacian. These operators are classical generalisations of the fractional Laplacian. The existence result is shown under a nonlocal version of the Keller-Osserman condition, stated in terms of the subordinator and the source term $f$.