Inserted: 17 jul 2021
Last Updated: 13 oct 2021
Journal: Mathematics in Engineering
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.