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

• Lucio Damascelli ^[2] ; Filomena Pacella ^[1]
  1. [1] Università de Roma La Sapienza

     Università de Roma La Sapienza

     Roma Capitale, Italia

     
  2. [2] Università di Roma "Tor Vergata", Italia
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 26, Nº 4, 1998, págs. 689-707
• Idioma: inglés
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• Resumen

  • In this paper we prove some monotonicity and symmetry properties of positive solutions of the equation - div Du) = f (u) satisfying an homogenuous Dirichlet boundary condition in a bounded domain Q. 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 Q is a ball then the solutions are radially symmetric and strictly radially decreasing.