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Minimality of balls in the small volume regime for a general Gamow-type functional

  • Davide Carazzato ORCID logo , Nicola Fusco and Aldo Pratelli ORCID logo EMAIL logo
Published/Copyright: December 1, 2021

Abstract

We consider functionals given by the sum of the perimeter and the double integral of some kernel g : N × N + , multiplied by a “mass parameter” ε. We show that, whenever g is admissible, radial and decreasing, the unique minimizer of this functional among sets of given volume is the ball as soon as ε 1 .

MSC 2010: 49J21

Communicated by Irene Fonseca


References

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Received: 2020-11-25
Revised: 2021-09-23
Accepted: 2021-10-08
Published Online: 2021-12-01
Published in Print: 2023-04-01

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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