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.
Flat level set regularity of p-Laplace phase transitions / E. Valdinoci, B. Sciunzi, V.O. Savin. - In: MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0065-9266. - 182:858(2006), pp. 1-150. [10.1090/memo/0858]
Flat level set regularity of p-Laplace phase transitions
E. ValdinociPrimo
;
2006
Abstract
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.
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