Title: An isoperimetric problem involving the competition between the perimeter and a nonlocal perimeter
Abstract: In this talk, I will present an isoperimetric problem in which the perimeter is replaced by $P-\gamma P_\varepsilon$, where $\gamma\in(0,1)$, $P$ stands for the classical perimeter and $P_\varepsilon$ is a nonlocal energy which converges to the perimeter as $\varepsilon$ vanishes. This problem is derived from Gamow’s liquid drop model for the atomic nucleus in the case where the repulsive potential is sufficiently decaying at infinity and in the large mass regime. I will discuss existence, uniform regularity of quasi-minimizers, and characterize minimizers for small $\varepsilon$.
