Comparison results for a nonlocal singular elliptic problem

2022/11/15 by Brandolini, Barbara, de Bonis, Ida, Ferone, Vincenzo +1 · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2211.08066

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.

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• First Eigenvalue and Torsional Rigidity: Isoperimetric Inequalities for the Fractional Laplacian
• Nonlocal singular problem and associated Sobolev type inequality with extremal in the Heisenberg group

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