The Monge-Amp\`ere Equation
Abstract
In this survey article we discuss the interior and boundary regularity of Alexandrov solutions to D2u = 1. We include some topics which it seems were not recently revisited in similar articles, including Calabi's interior C3 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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