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

Le, Nam; Savin, Ovidiu

doi:10.1090/S0002-9939-2014-12340-9

On boundary Hölder gradient estimates for solutions to the linearized Monge-Ampère equations
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by Nam Q. Le and Ovidiu Savin PDF

Proc. Amer. Math. Soc. 143 (2015), 1605-1615 Request permission

Abstract:

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 $C^{1,\gamma }$ 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.

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