We consider functionals given by the sum of the perimeter and the double integral of some kernel g : ℝN × ℝN → ℝ+, 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
Minimality of balls in the small volume regime for a general Gamow-type functional
Carazzato, Davide;Pratelli, Aldo
2023
Abstract
We consider functionals given by the sum of the perimeter and the double integral of some kernel g : ℝN × ℝN → ℝ+, 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 ≪ 1File in questo prodotto:
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CFP_pub.pdf
embargo fino al 01/01/2025
Descrizione: Paper in collaboration with Nicola Fusco and Aldo Pratelli
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