Enrico Valdinoci, Berardino Sciunzi, Vasile Ovidiu Savin
Flat level set regularity
of $p$-Laplace phase transitions
(1538K, LaTeX)

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.