SC - 1014 | Flat Level Set Regularity of P-laplace Phase Transitions

Flat Level Set Regularity of P-laplace Phase Transitions (Memoirs of the American Mathematical Society) by Enrico Valdinoci (Author), Berardino Sciunzi (Author), and Vasile Ovidiu Savin (Author)

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.

2006 | ISBN: 0821839101 | ID: SC - 1014