TITLE

# Monotonicity and one-dimensional symmetry for solutions of -? u = f( u) in half-spaces

AUTHOR(S)
Farina, Alberto; Montoro, Luigi; Sciunzi, Berardino
PUB. DATE
January 2012
SOURCE
Calculus of Variations & Partial Differential Equations;Jan2012, Vol. 43 Issue 1/2, p123
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
We prove a weak comparison principle in narrow domains for sub-super solutions to -? u = f( u) in the case 1 < p = 2 and f locally Lipschitz continuous. We exploit it to get the monotonicity of positive solutions to -? u = f( u) in half spaces, in the case $${\frac{2N+2}{N+2} < p\leq 2}$$ and f positive. Also we use the monotonicity result to deduce some Liouville-type theorems. We then consider a class of sign-changing nonlinearities and prove a monotonicity and a one-dimensional symmetry result, via the same techniques and some general a-priori estimates.
ACCESSION #
67363488

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