Abstract

Nearly 20 years ago, Heiko von der Mosel and the speaker have launched a series of projects to analyze several nonlocal energies of non-smooth sets S, defined as multiple integrals of various geometrically defined quantities, depending on two or more points of S. One of the prominent examples is the tangent-point energy.

I will present a survey of regularity results concerning this particular energy, and sketch a new, pretty natural proof of the characterization of finite energy sets in terms of fractional Sobolev spaces.