Calculus of Variations and Geometric Measure Theory

E. Cinti - R. Ognibene - B. Ruffini

A quantitative stability inequality for fractional capacities

created by ruffini on 17 Jul 2021
modified on 13 Oct 2021


Published Paper

Inserted: 17 jul 2021
Last Updated: 13 oct 2021

Journal: Mathematics in Engineering
Pages: 27
Year: 2021


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.