Degenerate elliptic equations with nonlinear boundary conditions and measures data

Andreu, Fuensanta; Igbida, Noureddine; Mazón, José M.; Toledo, Julián

Geodesic

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Degenerate elliptic equations with nonlinear boundary conditions and measures data

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

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 8 (2009) no. 4, pp. 767-803

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Résumé

In this paper we study the questions of existence and uniqueness of solutions for equations of type $- div 𝐚 (x, D u) + γ (u) ∋ μ_{1}$ , posed in an open bounded subset $Ω$ of $ℝ^{N}$ , with nonlinear boundary conditions of the form $𝐚 (x, D u) \cdot η + β (u) ∋ μ_{2}$ . The nonlinear elliptic operator $div 𝐚 (x, D u)$ is modeled on the $p$ -Laplacian operator $Δ_{p} (u) = div ({|D u|}^{p - 2} D u)$ , with $p > 1$ , $γ$ and $β$ are maximal monotone graphs in $ℝ^{2}$ such that $0 \in γ (0) \cap β (0)$ and the data $μ_{1}$ and $μ_{2}$ are measures.

MR Zbl

Classification : 35J60, 35D05

Affiliations des auteurs :

Andreu, Fuensanta ¹ ; Igbida, Noureddine ² ; Mazón, José M. ¹ ; Toledo, Julián ¹

@article{ASNSP_2009_5_8_4_767_0,
     author = {Andreu, Fuensanta and Igbida, Noureddine and Maz\'on, Jos\'e M. and Toledo, Juli\'an},
     title = {Degenerate elliptic equations with nonlinear boundary conditions and measures data},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {767--803},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 8},
     number = {4},
     year = {2009},
     mrnumber = {2647911},
     zbl = {1205.35120},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ASNSP_2009_5_8_4_767_0/}
}

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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://geodesic.mathdoc.fr/item/ASNSP_2009_5_8_4_767_0/