# Optimal regularity for supercritical parabolic obstacle problems – Damià Torres (Universitat de Barcelona)

Aula Magna

#### Abstract

The parabolic nonlocal obstacle problem is said to be in the supercritical regime (s < 1/2) when the time derivative is of higher order than the diffusion operator. We will discuss the optimal $C^{1,1}$ regularity of solutions and the $C^{1,α}$ regularity of the free boundary. The arguments rely on comparison principles and the scaling of the equation to circumvent the fact that blow-ups, the usual technique for free boundary problems, are not useful in this context.

This is a joint work with X. Ros-Oton.

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