An Isoperimitric problem perturbed by the potential of the reproduction kernel of a reproducing kernel Hilbert space.

Résumé

The purpose of This paper is to study the minimizer of the isoperi
metric perturbation problem, over measurable sets of fixed volume.
The problem is perturbed by an addition of repulsive nonlocal potentials of kernel K, which is a reproduction kernel of a reproducing kernel Hilbert space. We establish the existence of a minimizer of this problem. Besides, we study the geometric shape of a minimizer.