Calculus of Variations and Geometric Measure Theory

F. Santambrogio - V. Vespri

Continuity in two dimensions for a very degenerate elliptic equation

created by santambro on 20 Jun 2009
modified on 15 Aug 2010


Accepted Paper

Inserted: 20 jun 2009
Last Updated: 15 aug 2010

Journal: Nonlinear Analysis A
Year: 2010


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

Keywords: regularity, Degenerate elliptic PDEs