The Monge-Amp\`{e}re Equation

By Connor Mooney. 2018

161 citations recorded by the source corpus.

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'Universita degli Studi di Torino, and the other for the Oxford PDE CDT.

View Paper: https://www.semanticscholar.org/paper/adb256760c4a7695cffc65394482245fc07ccfc3

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Citations in the corpus

• Computational Optimal Transport (2018, background): “There is a large body of literature on the theoretical analysis of the Monge–Ampère equation, and in particular the regularity of its solution—see, for instance, [Gutiérrez, 2016]; we refer the interested read to the review paper by Caffarelli [2003].”