The elastica functional as the critical Gamma-limit of the screened Gamow model

Theresa Simon (Universität Münster) #

I will consider the large mass limit of a nonlocal isoperimetric problem in two dimensions with screened Coulomb repulsion. In this regime, the competition between perimeter and the repulsion simplifies to leading order by the nonlocal interaction localizing on the boundary of the sets. For an appropriate choice of screening constant, the perimeter is exactly cancelled, requiring an analysis of the next order contribution. It turns out that then the nature of the problem changes from length minimization to curvature minimization: I will prove that the Gamma limit is given by (the relaxation of) the elastica functional, i.e., the integral over the squared curvature over the boundary. This is joint work with Cyrill Muratov and Matteo Novaga.