On boundary Hölder gradient estimates for solutions to the linearized Monge-Ampère equations

Abstract

In this paper, we establish boundary Hölder gradient estimates for solutions to the linearized Monge-Ampère equations with $L^p$ ($n<p\le \infty$) right hand side and $C^{1,\gamma }$ boundary values under natural assumptions on the domain, boundary data and the Monge-Ampère measure. These estimates extend our previous boundary regularity results for solutions to the linearized Monge-Ampère equations with bounded right hand side and $C^{1,1}$ boundary data.

to appear in Proc. Amer. Math. Soc

References in corpus (2)

• Global $W^{2,p}$ estimates for the Monge-Ampere equation
• Boundary regularity for solutions to the linearized Monge-Ampère equations