A nonlocal isoperimetric problem: density perimeter.

Abstract: We will discuss a variant of a classical geometric minimization problem, known as the “nonlocal isoperimetric problem”, which arises from studies in Nuclear Physics by Gamow in the 1930’s. By introducing a density in the perimeter functional, we obtain features that differ substantially from existing results in the framework of the classical problem without densities. In the regime of “small” non-local contribution, we completely characterize the minimizer, in the case the density is a monomial radial weight.