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Continuity in two dimensions for a very degenerate elliptic equation

Authors:	Filippo Santambrogio Vincenzo Vespri

Institution:	^a CEREMADE, UMR CNRS 7534, Université Paris-Dauphine, Pl. de Lattre de Tassigny, 75775 Paris Cedex 16, France ^b Dipartimento di Matematica Ulisse Dini, Universitá degli studi di Firenze, Viale Morgagni, 67/a 50134 Firenze, Italy

Abstract:	An elliptic equation ∇⋅(F(∇u))=f whose ellipticity strongly degenerates for small values of ∇u (say, F=0 on B(0,1)) is considered. The aim is to prove regularity for F(∇u). The paper proves a continuity result in dimension 2 and presents some applications.

Keywords:	Nonlinear very degenerate elliptic equation Bidimensional case Local continuity of the gradient Traffic congestion
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