Continuity in two dimensions for a very degenerate elliptic equation

Santambrogio, Filippo; Vespri, Vincenzo

Santambrogio, Filippo; Vespri, Vincenzo (2010), Continuity in two dimensions for a very degenerate elliptic equation, Nonlinear Analysis: Theory, Methods & Applications, 73, 12, p. 3832-3841. http://dx.doi.org/10.1016/j.na.2010.08.008

Type

Article accepté pour publication ou publié

External document link

http://arxiv.org/abs/0909.2848v1

Date

2010

Journal name

Nonlinear Analysis: Theory, Methods & Applications

Volume

Number

Publisher

Elsevier

Pages

3832-3841

Abstract (EN)

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.

Subjects / Keywords

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