Flat Level Set Regularity of P-laplace Phase Transitions
Enrico Valdinoci
144 pages, Paperback
ISBN: 0821839101
ISBN13:
Language: English
Publish: 1149490800000
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.