Monotonicity and symmetry of solutions of $p$-Laplace equations, $1<p<2$, via the moving plane method

Damascelli, Lucio, and Pacella, Filomena. "Monotonicity and symmetry of solutions of \( p \)-Laplace equations, \( 1 < p < 2 \), via the moving plane method." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 9.2 (1998): 95-100. <http://eudml.org/doc/252359>.

@article{Damascelli1998,
abstract = {We present some monotonicity and symmetry results for positive solutions of the equation \( - \text\{div\} ( |Du| ^\{p-2\} Du ) = f (u) \) satisfying an homogeneous Dirichlet boundary condition in a bounded domain \( \Omega \). We assume 1 < p < 2 and \( f \) locally Lipschitz continuous and we do not require any hypothesis on the critical set of the solution. In particular we get that if \( \Omega \) is a ball then the solutions are radially symmetric and strictly radially decreasing.},
author = {Damascelli, Lucio, Pacella, Filomena},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {p-Laplace equations; Monotonicity and symmetry of positive solutions; Moving plane method; -Laplace equations; monotonicity and symmetry of solutions of -Laplace equations; moving plane method},
language = {eng},
month = {6},
number = {2},
pages = {95-100},
publisher = {Accademia Nazionale dei Lincei},
title = {Monotonicity and symmetry of solutions of \( p \)-Laplace equations, \( 1 < p < 2 \), via the moving plane method},
url = {http://eudml.org/doc/252359},
volume = {9},
year = {1998},
}

TY - JOUR
AU - Damascelli, Lucio
AU - Pacella, Filomena
TI - Monotonicity and symmetry of solutions of \( p \)-Laplace equations, \( 1 < p < 2 \), via the moving plane method
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1998/6//
PB - Accademia Nazionale dei Lincei
VL - 9
IS - 2
SP - 95
EP - 100
AB - We present some monotonicity and symmetry results for positive solutions of the equation \( - \text{div} ( |Du| ^{p-2} Du ) = f (u) \) satisfying an homogeneous Dirichlet boundary condition in a bounded domain \( \Omega \). We assume 1 < p < 2 and \( f \) locally Lipschitz continuous and we do not require any hypothesis on the critical set of the solution. In particular we get that if \( \Omega \) is a ball then the solutions are radially symmetric and strictly radially decreasing.
LA - eng
KW - p-Laplace equations; Monotonicity and symmetry of positive solutions; Moving plane method; -Laplace equations; monotonicity and symmetry of solutions of -Laplace equations; moving plane method
UR - http://eudml.org/doc/252359
ER -