A strongly degenerate quasilinear equation : the elliptic case
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Volume 3 (2004) no. 3, p. 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
@article{ASNSP_2004_5_3_3_555_0,
     author = {Andreu, Fuensanta and Caselles, Vicent and Maz\'on, Jos\'e},
     title = {A strongly degenerate quasilinear equation : the elliptic case},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 3},
     number = {3},
     year = {2004},
     pages = {555-587},
     zbl = {1117.35022},
     mrnumber = {2099249},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2004_5_3_3_555_0}
}
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, Volume 3 (2004) no. 3, pp. 555-587. http://www.numdam.org/item/ASNSP_2004_5_3_3_555_0/

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