Inserted: 20 jun 2009
Last Updated: 15 aug 2010
Journal: Nonlinear Analysis A
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