English

The Monge-Amp\`{e}re Equation

Analysis of PDEs 2018-06-27 v1

Abstract

In this survey article we discuss the interior and boundary regularity of Alexandrov solutions to detD2u=1\det D^2u = 1. We include some topics which it seems were not recently revisited in similar articles, including Calabi's interior C3C^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.

Keywords

Cite

@article{arxiv.1806.09945,
  title  = {The Monge-Amp\`{e}re Equation},
  author = {Connor Mooney},
  journal= {arXiv preprint arXiv:1806.09945},
  year   = {2018}
}
R2 v1 2026-06-23T02:42:09.780Z