The structure of the regular and the singular set of the free boundary in the obstacle problem for fractional heat equation.

Abstract: In this talk, I will discuss the structure of the free boundary in the obstacle problem for fractional powers of the heat operator. Our results are derived from the study of a lower dimensional obstacle problem for a class of local, but degenerate, parabolic equations. The analysis will be based on new Almgren, Weiss and Monneau type monotonicity formulas and the associated blow-up analysis. This is a joint work with D. Danielli, N. Garofalo and A. Petrosyan.

analysis of PDEs

Audience: researchers in the topic

CMI seminar series

Series comments: Please visit the seminar series homepage for streaming details. Timings of the seminar vary from week to week.