Regularity theory for PDE and free boundary problemsColloquium CRC 1720

by Xavier Ros-Oton

Tuesday Apr 21, 2026, 2:15 PM → 3:15 PM Europe/Berlin

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

One of the most basic and important questions in PDE is that of regularity: to decide whether all solutions to a given PDE are smooth or not. A classical example is Hilbert’s 19th problem, solved in 1956 by De Giorgi and Nash. The regularity theory for elliptic and parabolic PDE experienced a huge development during the second half of the 20th century, and nowadays there are still several problems of crucial importance that remain open. The aim of this talk is to give an overview of this topic and present some recent results in this direction.