Geodesic
Monotonicity and symmetry of solutions of \( p \)-Laplace equations, \( 1 p 2 \), via the moving plane method
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 9 (1998) no. 2, pp. 95-100.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

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.
Dimostriamo alcuni risultati di monotonia e simmetria per soluzioni positive dell’equazione \( - \text{div} ( |Du| ^{p-2} Du ) = f (u) \) con condizioni di Dirichlet omogenee sul bordo in un dominio limitato \( \Omega \). Supponiamo che 1 p 2 e che \( f \) sia localmente Lipschitziana e non facciamo alcuna ipotesi sui punti critici della soluzione. In particolare otteniamo che se \( \Omega \) e` una palla le soluzioni sono radiali e radialmente strettamente decrescenti. 
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     title = {Monotonicity and symmetry of solutions of \( p {\)-Laplace} equations, \( 1 < p < 2 \), via the moving plane method},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
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Damascelli, Lucio; 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. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 9 (1998) no. 2, pp. 95-100. http://geodesic.mathdoc.fr/item/RLIN_1998_9_9_2_a3/

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