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Carnegie Mellon NSF logoCenter for Nonlinear Analysis
Alexis Vasseur
Afilliation: University of Texas at Austin

Title: Integral Variational Problems

Abstract: We will present, in this talk, the proof of the existence of classical solutions for a class of non-linear integral variational problems. Those types of equations are typically used in nonlocal image and signal processing. They involve nonlinear versions of fractional diffusion operators. The method is based on De Giorgi-Nash-Moser techniques. It extends to fully nonlinear settings a previous work on the regularity of solutions to the Surface Quasi-Geostrophic equations (SQG). This is a joint work with L. Caffarelli and Ch.-H. Chan.

Slides: VasseurAlexis.pdf