Degenerate Elliptic Equations with Nonlinear Boundary Conditions and Measures Data

• Fuensanta Andreu ^[1] ; Noureddine Igbida ^[2] ; José M. Mazón ^[1] ; Julián Toledo ^[1]
  1. [1] Universitat de València

     Universitat de València

     Valencia, España

     
  2. [2] University of Picardie Jules Verne

     University of Picardie Jules Verne

     Arrondissement d’Amiens, Francia

     
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 8, Nº 4, 2009, págs. 767-803
• Idioma: inglés
• DOI: 10.2422/2036-2145.2009.4.06
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• Resumen

  • In this paper we study the questions of existence and uniqueness of solutions for equations of type −div a(x , Du) + γ (u) 3 µ1 , posed in an open bounded subset Q of RN , with nonlinear boundary conditions of the form a(x , Du)·η +β(u) 3 µ2 . The nonlinear elliptic operator div a(x , Du) is modeled on the p-Laplacian operator tl. p (u) = div (|Du| p−2 Du), with p > 1, γ and β are maximal monotone graphs in R2 such that 0 ∈ γ (0) ∩ β(0) and the data µ1 and µ2 are measures.