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arXiv · 1303.3305

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

Nam Q. Le·Ovidiu Savin
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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 $C^{1,γ}$ 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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Nam Q. Le, Ovidiu Savin. 2013-08-24. On boundary Hölder gradient estimates for solutions to the linearized Monge-Ampère equations. https://arxiv.org/abs/1303.3305

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