Seminario Análisis y EDPs

Free boundary problems as Hamilton-Jacobi-Bellman equations

Ponente:  Néstor Guillén (Texas State University)
Fecha:  miércoles 03 de marzo de 2021 - 15:00
Lugar:  Online - Info:

Integro-differential equations have been fundamental in the analysis of all kinds of free boundary problems, from the vortex patch equation to interfacial Darcy flows. In work with Chang-Lara and Schwab, we show how certain two-phase free boundary problems such as the quasistatic Stefan problem are equivalent to nonlocal Hamilton-Jacobi-Bellman equations. This equivalence has a number of immediate consequences, such as an existence and uniqueness theory based on viscosity solutions, and propagation of Lipschitz regularity of the initial data