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Singular solutions to the Monge-Ampere equation

  • Connor Mooney (ETH Zürich)
G3 10 (Lecture hall)

Abstract

The Monge-Ampere equation det D^2u = 1 arises in several applications. Examples of Pogorelov show that interior regularity is not expected in general. We will discuss optimal estimates on the Hausdorff dimension of the singular set, and sharp integrability conditions for the second derivatives that rule out singularities. Some of this is joint work with T. Collins.

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

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