We consider functionals given by the sum of the perimeter and the double integral of some kernel g : R-N x R-N -> R+, multiplied by a "mass parameter" epsilon. 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 epsilon << 1.
Minimality of balls in the small volume regime for a general Gamow-type functional
Pratelli, A
2023-01-01
Abstract
We consider functionals given by the sum of the perimeter and the double integral of some kernel g : R-N x R-N -> R+, multiplied by a "mass parameter" epsilon. 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 epsilon << 1.File in questo prodotto:
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