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Research Article | Open Access

A quantitative stability inequality for fractional capacities

Eleonora Cinti1, Roberto Ognibene2, Berardo Ruffini1( )
Dipartimento di Matematica, Università di Bologna, 40126 Bologna, Italy
Dipartimento di Ingegneria meccanica energetica, gestionale e dei trasporti, Università di Genova, 16145 Genova, Italy
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Abstract

The aim of this work is to show a non-sharp quantitative stability version of the fractional isocapacitary inequality. In particular, we provide a lower bound for the isocapacitary deficit in terms of the Fraenkel asymmetry. In addition, we provide the asymptotic behaviour of the s-fractional capacity when s goes to 1 and the stability of our estimate with respect to the parameter s.

Keywords

capacityfractional Laplacianquantitative inequalitiesCaffarelli-Silvestre extension

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Mathematics in Engineering
Volume 4 Issue 5,
October 2022
Pages 1-28
DOI: 10.3934/mine.2022044

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Cite this article:
Cinti E, Ognibene R, Ruffini B. A quantitative stability inequality for fractional capacities. Mathematics in Engineering, 2022, 4(5): 1-28. https://doi.org/10.3934/mine.2022044

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Received: 17 July 2021
Accepted: 04 October 2021
Published: 15 October 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)