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arXiv · 2107.08257

A quantitative stability inequality for fractional capacities

Eleonora Cinti·Roberto Ognibene·Berardo Ruffini
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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 $s$.

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Eleonora Cinti, Roberto Ognibene, Berardo Ruffini. 2021-07-17. A quantitative stability inequality for fractional capacities. https://arxiv.org/abs/2107.08257

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