BZ Seminar in Analysis: Herbert Koch (Universität Bonn)

Rough solutions to parabolic equations

Maximal functions and square functions are basic tools of harmonic analysis. Solutions to linear elliptic boundary value problems and parabolic initial value problems can be used to construct maximal functions and square functions. This point of view has been useful in the context of the Navier-Stokes equations in my work with Daniel Tataru, and in the treatment of harmonic functions in Lipschitz domains by Dahlberg, Kenig and their coworkers. Here I will present results with T. Lamm on an application of these ideas to quasilinear and fully nonlinear parabolic equations. Particular examples are the Ricci-de Turck flow, the harmonic map heat flow as well as linearisations of the front of the porous medium equation and the thin film equation.

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