Seminar Analysis: Xavier Ros-Oton (University of Zürich)

Regularity of free boundaries in obstacle problems for integro-differential operators

We present a brief overview of the regularity theory for free boundaries in different obstacle problems. We describe how a monotonicity formula of Almgren plays a central role in the study of the regularity of the free boundary in some of these problems. Finally, we explain new strategies which we have recently developed to deal with cases in which monotonicity formulas are not available.

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