De Giorgi's method: in(s) and out(s)

Jana Bjorn

(Linköping University)

Event: ERC Workshop on Geometric Analysis on sub-Riemannian and Metric Spaces

Date: Oct 13, 2011, time: 09:30

Place: Centro De Giorgi, Scuola Normale Superiore

Abstract. One of the main break-throughs in the 20th century mathematics was De Giorgi's proof of Hölder continuity for solutions of elliptic PDEs. His method has since then been used to prove interior regularity in various contexts.
It is maybe less known, though not entirely surprising that De Giorgi's method also yields sufficient conditions for boundary regularity.
In the talk, I will discuss a recent variation of De Giorgi's method which goes in the opposite direction, leading to a necessary condition for boundary regularity of PDEs and variational integrals.