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.
| ISBN: | 9780821839102 |
| Publication date: | 30th June 2006 |
| Author: | Enrico Valdinoci, Berardino Sciunzi, Vasile Ovidiu Savin |
| Publisher: | American Mathematical Society |
| Format: | Paperback |
| Pagination: | 144 pages |
| Series: | Memoirs of the American Mathematical Society |
| Genres: |
Calculus and mathematical analysis Mathematics |