Partial regularity in nonlocal problems

Giuseppe Mingione (U of Parma)

Feb 28. 2025, 09:30 — 10:20

The theory of partial regular regularity for elliptic systems replaces the classical De Giorgi-Nash-Moser one for scalar equations asserting that solutions are regular outside a negligible closed subset called the singular set. Eventually, Hausdorff dimension estimates on such a set can be given. The singular set is in general non-empty. The theory is classical, started by Giusti & Miranda and Morrey, in turn relying on De Giorgi's seminal ideas for minimal surfaces. I shall present a few results aimed at extending the classical, local partial regularity theory to nonlinear integrodifferential systems and to provide a few basic, general tools in order to prove so called epsilon-regularity theorems in general non-local settings. From recent, joint work with Cristiana De Filippis (Parma) and Simon Nowak (Bielefeld). 

Further Information
Venue:
ESI Boltzmann Lecture Hall
Recordings:
Recording
Associated Event:
Degenerate and Singular PDEs (Workshop)
Organizer(s):
Verena Bögelein (PLUS, Salzburg)
Ugo Gianazza (U of Pavia)
Juha Kinnunen (Aalto U)
Naian Liao (PLUS, Salzburg)