We prove a weak comparison principle in narrow domains for sub-super solutions to -Delta(p)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 -Delta(p)u = f(u) in half spaces, in the case 2N+2/N+ 2 < p <= 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.
Monotonicity and one-dimensional symmetry for solutions of -Delta(p)u = f(u) in half-spaces / Farina, A; Montoro, Luigi; Sciunzi, Berardino. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 43:1-2(2012), pp. 123-145.
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Titolo: | Monotonicity and one-dimensional symmetry for solutions of -Delta(p)u = f(u) in half-spaces |
Autori: | |
Data di pubblicazione: | 2012 |
Rivista: | |
Citazione: | Monotonicity and one-dimensional symmetry for solutions of -Delta(p)u = f(u) in half-spaces / Farina, A; Montoro, Luigi; Sciunzi, Berardino. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 43:1-2(2012), pp. 123-145. |
Handle: | http://hdl.handle.net/20.500.11770/138560 |
Appare nelle tipologie: | 1.1 Articolo in rivista |