On certain degenerate and singular elliptic PDEs II: Divergence-form operators, Harnack inequalities, and applications

Abstract

By means of the Monge–Ampère real-analysis and PDE techniques associated to certain convex functions, an approach towards Harnack inequalities is developed that simultaneously extends the one for uniformly elliptic operators from the De Giorgi–Nash–Moser theory and the one for the linearized Monge–Ampère operator from the Caffarelli–Gutiérrez theory. Applications include regularity properties for solutions to divergence-form elliptic equations with power-like singularities and C2-estimates for solutions to the Monge–Ampère equation.