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

In this paper, we establish boundary Hölder gradient estimates for solutions to the linearized Monge-Ampère equations with $L^{p}$ ($n<p\leq\infty$) right hand side and $C^{1,γ}$ 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.

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