Seminario Análisis y EDPs

1D symmetry of solutions to a class of semilinear one-phase elliptic PDE

Ponente:  Alessandro Audrito (ETH)
Fecha:  miércoles 13 de octubre de 2021 - 15:00
Lugar:  Online - (ID: 814 9107 9139; Access code: 937701)


We study minimizers of a family of functionals arising in combustion theory, which converge, for infinitesimal values of the parameter, to minimizers of the emph{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 $RR^N$ 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).