Calculus of variations for nonlocal Sobolev–Bregman forms

19.11.2025, 13:00 Uhr  –  Haus 9, Raum 0.17
Forschungsseminar Diskrete Spektraltheorie

Artur Rutkowski

The Sobolev–Bregman integral forms are an \(L^p\) version of quadratic forms defining the fractional Sobolev spaces \(H^s\), that emerged in a natural way from the probabilistic potential theory in \(L^p\). The forms are strongly nonlinear, in the sense that their natural domain is not linear. Despite that, we prove existence of minimizers for the exterior value problem, and using a special choice of curves we establish an Euler–Lagrange equation for the minimizers. We also prove a Green-type formula and investigate the domain of the polarized form, which is surprisingly challenging. Based on joint work with Krzysztof Bogdan, Katarzyna Pietruska-Pałuba and Christian Rose.