Degenerate elliptic equations with nonlinear boundary conditions and measures data
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 8 (2009) no. 4, pp. 767-803.

In this paper we study the questions of existence and uniqueness of solutions for equations of type -div𝐚(x,Du)+γ(u)μ 1 , posed in an open bounded subset Ω of N , with nonlinear boundary conditions of the form 𝐚(x,Du)·η+β(u)μ 2 . The nonlinear elliptic operator div𝐚(x,Du) is modeled on the p-Laplacian operator Δ p (u)=div(Du p-2 Du), with p>1, γ and β are maximal monotone graphs in 2 such that 0γ(0)β(0) and the data μ 1 and μ 2 are measures.

Classification : 35J60, 35D05
Andreu, Fuensanta 1 ; Igbida, Noureddine 2 ; Mazón, José M. 1 ; Toledo, Julián 1

1 Departamento de Análisis Matemático, Universitat de València, Dr. Moliner 50, 46100 Burjassot (Valencia), Spain
2 LAMFA, CNRS-UMR 6140, Université de Picardie Jules Verne, 33 rue Saint Leu, 80038 Amiens, France
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     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
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Andreu, Fuensanta; Igbida, Noureddine; Mazón, José M.; Toledo, Julián. Degenerate elliptic equations with nonlinear boundary conditions and measures data. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 8 (2009) no. 4, pp. 767-803. http://archive.numdam.org/item/ASNSP_2009_5_8_4_767_0/

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