On evolution equations with fractional diffusion

PDE Seminar
Tuesday, November 9, 2010 - 3:05pm
1 hour (actually 50 minutes)
Skiles 255
University of Chicago
We prove a new Holder estimate for drift-(fractional)diffusion equations similar to the one recently obtained by Caffarelli and Vasseur, but for bounded drifts that are not necessarily divergence free. We use this estimate to study the regularity of solutions to either the Hamilton-Jacobi equation or conservation laws with critical fractional diffusion.