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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium
Luis Silvestre
University of Chicago
Title: Smooth solutions for the Hamilton-Jacobi equation with critical fractional diffusion

Abstract: We study the Hamilton-Jacobi equation with fractional diffusion. If the power of the Laplacian in the diffusion is larger than 1/2, the effects of the diffusion is stronger than the first order term and the equation is well posed. If the power of the Laplacian is less than 1/2, the solution is Lipschitz, but may not be differentiable. For the critical case of the Laplacian to the 1/2, we prove that the equation is also well posed in the classical sense. The result is derived using a new Holder estimate for reaction-(fractional)diffusion equations similar to the one recently obtained by Caffarelli and Vasseur, but for bounded vector fields that are not necessarily divergence free. We will also discuss its application to the parabolic Isaacs-Bellman equation of order one.

Date: Tuesday, March 16, 2010
Time: 1:30 pm
Location: PPB 300