Memoirs of the American Mathematical Society

1 total work

Flat Level Set Regularity of p-Laplace Phase Transitions

by Enrico Valdinoci, Berardino Sciunzi, and Vasile Ovidiu Savin

Published 1 July 2006

We prove a Harnack inequality for level sets of $p$-Laplace phase transition minimizers. In particular, if a level set is included in a flat cylinder, then, in the interior, it is included in a flatter one. The extension of a result conjectured by De Giorgi and recently proven by the third author for $p=2$ follows.