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arXiv · 1810.10688

Boundary H\"older gradient estimates for the Monge-Amp\`ere equation

Ovidiu Savin·Qian Zhang
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Abstract

We investigate global H\"older gradient estimates for solutions to the Monge-Amp\`ere equation $$\mathrm{det}\;D^2 u=f\quad\mathrm{in}\;\Omega,$$ where the right-hand side $f$ is bounded away from $0$ and $\infty$. We consider two main situations when a) the domain $\Omega$ is uniformly convex and b) $\Omega$ is flat.

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Ovidiu Savin, Qian Zhang. 2018-10-25. Boundary H\"older gradient estimates for the Monge-Amp\`ere equation. https://arxiv.org/abs/1810.10688

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