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 . We include some topics which it seems were not recently revisited in similar articles, including Calabi's interior 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}
}