Abstract
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.
Funder
Ministero dell’Istruzione, dell’Università e della Ricerca
Subject
Computational Mathematics,Control and Optimization,Control and Systems Engineering
Cited by
2 articles.
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