Interior $C^{2,\alpha }$ Regularity for the Quadratic Hessian Equation

Abstract

We establish interior $C^{2,\alpha }$ regularity for admissible solutions of the quadratic Hessian equation with positive $C^{\alpha }$ right-hand side on the full positive branch. The main ingredients are a quantitative large-trace propagation argument and an adaptive Dirichlet comparison method.