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.
Cinti, E., Ognibene, R., Ruffini, B. (2021). A quantitative stability inequality for fractional capacities. MATHEMATICS IN ENGINEERING, 4(5), 1-28 [10.3934/mine.2022044].
A quantitative stability inequality for fractional capacities
Ognibene R.;
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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