| Issue |
ESAIM: COCV
Volume 28, 2022
|
|
|---|---|---|
| Article Number | 4 | |
| Number of page(s) | 53 | |
| DOI | https://doi.org/10.1051/cocv/2021106 | |
| Published online | 11 January 2022 | |
A spherical rearrangement proof of the stability of a Riesz-type inequality and an application to an isoperimetric type problem★
Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”, Università degli Studi di Napoli Federico II,
80126
Napoli, Italy
** Corresponding author: giacomo.ascione@unina.it
Received:
18
May
2021
Accepted:
30
November
2021
We prove the stability of the ball as global minimizer of an attractive shape functional under volume constraint, by means of mass transportation arguments. The stability exponent is 1∕2 and it is sharp. Moreover, we use such stability result together with the quantitative (possibly fractional) isoperimetric inequality to prove that the ball is a global minimizer of a shape functional involving both an attractive and a repulsive term with a sufficiently large fixed volume and with a suitable (possibly fractional) perimeter penalization.
Mathematics Subject Classification: 49K40 / 49J40
Key words: Riesz rearrangement inequality / fractional perimeter / Riesz potential / quantitative isoperimetric inequality
© The authors. Published by EDP Sciences, SMAI 2022
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