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arXiv · 1806.09945

The Monge-Amp\`{e}re Equation

Connor Mooney
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Abstract

In this survey article we discuss the interior and boundary regularity of Alexandrov solutions to $\det D^2u = 1$. We include some topics which it seems were not recently revisited in similar articles, including Calabi's interior $C^3$ estimate, and the approaches of Cheng-Yau and Lions to obtain classical solutions to the Dirichlet problem. The survey grew from two mini-courses given by the author in May 2018. One was for "Advanced Lectures in Nonlinear Analysis" at l'Universit\`{a} degli Studi di Torino, and the other for the Oxford PDE CDT.

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Connor Mooney. 2018-06-26. The Monge-Amp\`{e}re Equation. https://arxiv.org/abs/1806.09945

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