We prove existence and uniqueness of entropy solutions for the Neumann problem for the quasilinear elliptic equation , where , , and is a convex function of with linear growth as , satisfying other additional assumptions. In particular, this class includes the case where , , being a convex function with linear growth as . 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 .
@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}, pages = {555--587}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 3}, number = {3}, year = {2004}, mrnumber = {2099249}, zbl = {1117.35022}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_2004_5_3_3_555_0/} }
TY - JOUR AU - Andreu, Fuensanta AU - Caselles, Vicent AU - Mazón, José TI - A strongly degenerate quasilinear equation : the elliptic case JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2004 SP - 555 EP - 587 VL - 3 IS - 3 PB - Scuola Normale Superiore, Pisa UR - http://archive.numdam.org/item/ASNSP_2004_5_3_3_555_0/ LA - en ID - ASNSP_2004_5_3_3_555_0 ER -
%0 Journal Article %A Andreu, Fuensanta %A Caselles, Vicent %A Mazón, José %T A strongly degenerate quasilinear equation : the elliptic case %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2004 %P 555-587 %V 3 %N 3 %I Scuola Normale Superiore, Pisa %U http://archive.numdam.org/item/ASNSP_2004_5_3_3_555_0/ %G en %F 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, Serie 5, Volume 3 (2004) no. 3, pp. 555-587. http://archive.numdam.org/item/ASNSP_2004_5_3_3_555_0/
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