@article{Cinti2022, 
author = {Eleonora Cinti and Roberto Ognibene and Berardo Ruffini},
title = {A quantitative stability inequality for fractional capacities},
year = {2022},
journal = {Mathematics in Engineering},
volume = {4},
number = {5},
pages = {1-28},
keywords = {capacity, fractional Laplacian, quantitative inequalities, Caffarelli-Silvestre extension},
url = {https://www.sciopen.com/article/10.3934/mine.2022044},
doi = {10.3934/mine.2022044},
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.}
}