Continuity in two dimensions for a very degenerate elliptic equation

Nonlinear Analysis, Theory, Methods and Applications

Volumn 73, Issue 12, 2010, Pages 3832-3841

  Santambrogio, Filippo ^a   Vespri, Vincenzo ^b  

^a UNIVERSITÉ PARIS DAUPHINE   (France)

^b UNIVERSITY OF FLORENCE   (Italy)

Author keywords

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

Indexed keywords

BIDIMENSIONAL CASE; DEGENERATE ELLIPTIC EQUATION; ELLIPTIC EQUATIONS; LOCAL CONTINUITY OF THE GRADIENT; TWO-DIMENSION;

GEOMETRY; TRAFFIC CONGESTION;

NONLINEAR EQUATIONS;

EID: 77956932758     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2010.08.008     Document Type: Article

References (9)

1. D. Gilbarg, and N. Trudinger Elliptic Partial Differential Equations of Second Order 1977 Springer-Verlag Berlin
2. E. De Giorgi Sulla differenziabilit e l'analiticit delle estremali degli integrali multipli regolari Mem. Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 3 3 1957 25 43
3. I. Fonseca, N. Fusco, and P. Marcellini An existence result for a nonconvex variational problem via regularity ESAIM Control Optim. Calc. Var. 7 2002 69 95
4. L. Esposito, G. Mingione, and C. Trombetti On the Lipschitz regularity for certain elliptic problems Forum Math. 18 2 2006 263 292
5. C. Carstensen, and S. Mller Local stress regularity in scalar nonconvex variational problems SIAM J. Math. Anal. 34 2002 495 509
6. L. Brasco, G. Carlier, and F. Santambrogio Congested traffic dynamics, weak flows and very degenerate elliptic equations J. Math. Pures Appl. 93 6 2010 652 671
7. E. DiBenedetto, and V. Vespri On the singular equation β (u ) t = Δ u Arch. Ration. Mech. Anal. 132 3 1995 247 309
8. E. DiBenedetto Degenerate Parabolic Equations Universitext 1993 Springer-Verlag New York
9. G. Carlier, C. Jimenez, and F. Santambrogio Optimal transportation with traffic congestion and Wardrop equilibria SIAM J. Control Optim. 47 2008 1330 1350