1:00 pm Wednesday, May 2, 2018
Analysis Seminar: Parabolic obstacle problems with critical scaling by Xavier Ros-Oton (University of Zurich) in RLM 10.176
Despite significant recent advances in the regularity theory for obstacle problems with integro-differential operators, some central questions remained open. On the one hand, there was a lack of understanding of parabolic problems with critical scaling, such as the obstacle problem for $\partial_t+(-\Delta)^{1/2}$. No regularity result for free boundaries was known for any parabolic problem with such scaling. On the other hand, optimal regularity estimates for solutions to nonlocal (elliptic and parabolic) obstacle problems relied strongly on monotonicity formulas, and therefore were only known in some specific cases. The aim of this talk is to present some new results which give a new approach to this theory, and allow us to answer these two important open questions. This is a joint work with Alessio Figalli and Joaquim Serra. Submitted by
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