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Math Colloquium
Camelia Pop
University of Pennsylvania
Title: The fractional Laplacian operator and its gradient perturbations

Abstract: The fractional Laplacian operator plays the same paradigmatic role in the theory of nonlocal operators that the Laplacian plays in the theory of local operators. We will present regularity results for solutions to problems defined by the fractional Laplacian operator with gradient perturbations. Our main results are the regularity of solutions in Sobolev spaces to the linear equation in the supercritical regime, when the operator is not elliptic, and the optimal regularity of solutions to the stationary obstacle problem in the supercritical regime. This is joint work with Charles Epstein and Arshak Petrosyan.

Date: Wednesday, January 21, 2015
Time: 4:30 pm
Location: Wean Hall 7218
Submitted by:  Bohman
Note: Please note room location. Refreshments at 4:00 pm, Wean Hall 6220