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

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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. 
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/
@article{RLIN_1998_9_9_2_a3,
     author = {Damascelli, Lucio and Pacella, Filomena},
     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},
     pages = {95--100},
     year = {1998},
     volume = {Ser. 9, 9},
     number = {2},
     zbl = {0923.35013},
     mrnumber = {MR1677254},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_1998_9_9_2_a3/}
}
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