A strongly degenerate quasilinear equation : the elliptic case
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 3 (2004) no. 3, pp. 555-587.

We prove existence and uniqueness of entropy solutions for the Neumann problem for the quasilinear elliptic equation u- div 𝐚(u,Du)=v, where vL 1 , 𝐚(z,ξ)= ξ f(z,ξ), and f is a convex function of ξ with linear growth as ξ, satisfying other additional assumptions. In particular, this class includes the case where f(z,ξ)=ϕ(z)ψ(ξ), ϕ>0, ψ being a convex function with linear growth as ξ. In the second part of this work, using Crandall-Ligget’s iteration scheme, this result will permit us to prove existence and uniqueness of entropy solutions for the corresponding parabolic problem with initial data in L 1 .

Classification : 35J60, 47H06, 47H20
Andreu, Fuensanta 1 ; Caselles, Vicent 2 ; Mazón, José 1

1 Universitat de Valencia Dept. de Análisis Matemático
2 Universitat Pompeu-Fabra Dept. de Tecnologia
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Andreu, Fuensanta; Caselles, Vicent; Mazón, José. A strongly degenerate quasilinear equation : the elliptic case. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 3 (2004) no. 3, pp. 555-587. http://archive.numdam.org/item/ASNSP_2004_5_3_3_555_0/

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