Calculus of Variations and Geometric Measure Theory
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E. Cinti - R. Ognibene - B. Ruffini

A quantitative stability inequality for fractional capacities

created by ruffini on 17 Jul 2021

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Submitted Paper

Inserted: 17 jul 2021
Last Updated: 17 jul 2021

Pages: 21
Year: 2021

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 $s$.


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