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

2020/09/08 by Carazzato, Davide, Fusco, Nicola, Pratelli, Aldo · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2009.03599

Abstract

We consider functionals given by the sum of the perimeter and the double integral of some kernel g:\mathbb R^N×\mathbb R^N→ \mathbb 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.

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• Existence and nonexistence results for a nonlocal isoperimetric problem on ℍⁿ
• Continuity of critical points for 1-dimensional non-local energies

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