Title: New monotonicity formulas for degenerate parabolic equations with applications to unique continuation and free boundary problems
Speaker: Agnid Banerjee (TIFR-CAM, Bengaluru)
Date: 08 March 2019
Time: 4:15 pm
Venue: LH-1, Mathematics Department
I will discuss a strong unique continuation theorem for zero order perturbations of the fractional heat equation
based on a monotonicity property of a generalized Almgren frequency in weighted Gauss space. This is a joint work
with Nicola Garofalo. If time permits, I will also talk on how such a truncated variant of the Almgren type
monotonicity formula combined with new Weiss and Monneau type monotonicity formulas allows to study the structure
of the singular set on the free boundary in the obstacle problem for the fractional heat operator.
This part of the talk ( if at all I get time !) is joint with Donatella Danielli, Nicola Garofalo and Arshak Petrosyan.