Departamento de Matemáticas UAM

Online Analysis and PDE seminar (UAM-UC-UC3M-UCM-ICMAT-IMUS)

Ponente: Alessandro Audrito (ETH, Zürich)

Fecha: Miércoles 13 de octubre de 2021 - 15:00

Enlace: us06web.zoom.us/j/81491079139?pwd=OWo1TWc0NEExNDJZUFljWVRIdkZRQT09

Resumen: We study minimizers of a family of functionals arising in combustion theory, which converge, for infinitesimal values of the parameter, to minimizers of the one-phase free boundary problem. We prove a $C^{1,alpha}$ estimate for the "interfaces" of  critical points  (i.e. the level sets separating the burnt and unburnt regions). As a byproduct, we obtain the one-dimensional symmetry of minimizers in the whole $R^N$ for $N le 4$, answering positively a conjecture of Fernández-Real and Ros-Oton. Our results are to the one-phase free boundary problem what Savin's results for the Allen-Cahn equation are to minimal surfaces.

 

This is a joint work with J. Serra (ETHZ).