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

Abstract We consider functionals given by the sum of perimeter and double integral some kernel g : ℝ N × → + {g:\mathbb{R}^{N}\times\mathbb{R}^{N}\to\mathbb{R}^{+}} , multiplied a “mass parameter” ε. show that, whenever g is admissible, radial decreasing, unique minimizer this functional among sets volume ball as soon ε ≪ 1 {\varepsilon\ll 1} .