The random fractional obstacle problem.Oberseminar Analysis

by Prof. Caterina Zeppieri (Universität Münster)

Thursday May 21, 2026, 2:15 PM → 4:15 PM Europe/Berlin

Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)

Nonlocal energies, such as fractional Sobolev seminorms, arise naturally in mathematical models involving long-range interactions. In this talk, we study minimizers of such energies that vanish on a collection of small balls with random centers and radii, leading to a bilateral (fractional) obstacle problem. I will present a homogenization result that holds under minimal assumptions on the distribution and size of the obstacles, which are generated by a stationary marked point process. In particular, the obstacles may overlap and form clusters with positive probability, giving rise to a complex microstructure. Our analysis identifies the limiting energy and shows how it reflects the underlying probability distribution of the obstacles. Joint work with Francesco Deangelis (University of Muenster) and Matteo Focardi (University of Florence).