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Comparison results for a nonlocal singular elliptic problem

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arxiv 2211.08066 v1 pith:IXYWP74T submitted 2022-11-15 math.AP

Comparison results for a nonlocal singular elliptic problem

Barbara Brandolini , Ida de Bonis , Vincenzo Ferone , Bruno Volzone This is my paper
classification math.AP
keywords resultscomparisonellipticnonlocalsingularalternativeargumentsbounded
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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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