On global solutions of the obstacle problem and the behaviour of the free boundary close to singularities of local solutions
Speaker
Georg Weiss, University of Duisburg-Essen
Time
2021-09-17 16:00 ~ 17:00, in 3 days
Venue
Online
VooV Meeting Info
VooV Meeting download website:
https://voovmeeting.com/index.html Conference ID: 563 822 261
Password: 210917
Abstract
Recently great progress has been achieved by Alessio Figalli et al. doing a fine analysis of the singular set in the obstacle problem. Much less is known about the behavior of the regular set close to singularities. The structure of this set may be very complicated, for example it may contain infinitely many connected components approaching the singularity, funnel-type singularities etc. The issue is related to the characterization of global solutions of the obstacle problem, that is solutions in the entire space. This characterization in turn is related to conjectures in potential analysis and an open problem since the 1980s. In this talk we will discuss progress in the characterization of global solutions and the application to singularities.
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