The Monge-Ampère Equation

2018/06/26 by Mooney, Connor
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1806.09945

Abstract

In this survey article we discuss the interior and boundary regularity of Alexandrov solutions to det 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'Università degli Studi di Torino, and the other for the Oxford PDE CDT.

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