Comparison results for a nonlocal singular elliptic problem

TL;DR

This paper establishes symmetrization and comparison results for fractional singular elliptic equations, providing new insights into solution regularity and energy estimates in bounded domains.

Contribution

It introduces novel symmetrization techniques and comparison results for fractional singular elliptic problems, offering a flexible approach beyond standard maximum principle methods.

Findings

Symmetrization results for fractional singular elliptic equations.

Lp regularity and energy estimates for solutions.

Comparison results depending on right-hand side summability.

Abstract

We provide symmetrization results in the form of mass concentration comparisons for fractional singular elliptic equations in bounded domains, coupled with homogeneous external Dirichlet conditions. Two types of comparison results are presented, depending on the summability of the right-hand side of the equation. The maximum principle arguments employed in the core of the proofs of the main results offer a nonstandard, flexible alternative to the ones described in [18, Theorem 31]. Some interesting consequences are Lp regularity results and nonlocal energy estimates for solutions.