Continuity in two dimensions for a very degenerate elliptic equation

Filippo Santambrogio (1) , Vincenzo Vespri (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 Dipartimento di Matematica "Ulisse Dini"

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

Domaines: Equations aux dérivées partielles [math.AP]

Filippo Santambrogio, Vincenzo Vespri. Continuity in two dimensions for a very degenerate elliptic equation. 2009. ⟨hal-00417372⟩