Graduate Analysis Seminar
Trevor Leslie
Instant Hölder Regularization of Advection Fractional-Diffusion Equations, Part I
Abstract: We examine an equation of the form $u_t + b\cdot \nabla u + (-\Delta)^s u = f$. A 2011 result by Luis Silvestre says that any bounded solution of the equation satisfies a certain Hölder estimate. In this talk, we prove an intermediate estimate that is used in the proof of Silvestre's main result. We also give an application of the result to a model in collective dynamics. The rest of the proof of the Hölder estimate will be given in a future talk (April 18) at the Graduate Analysis Seminar.
Wednesday March 21, 2018 at 4:00 PM in SEO 512