turkmath.org

In this talk, we discuss the Sobolev regularity of Monge potentials under the assumption that the initial measure is log-concave and the target measure has strictly positive density on an abstract Wiener space. We prove that the backward Monge potential is an element of the second-order Sobolev space. This regularity result allows us to show that the backward Monge potential solves the Monge-Ampére equation. We also prove that forward potential solves the Monge-Ampére equation in Alexandrov sense under weaker assumption than log-concavity.

Link to the seminar is:

https://teams.microsoft.com/l/meetup-join/19%3a0ae91f7b86a24e8fa1d818a6f74b22a1%40thread.tacv2/1651952054430?context=%7b%22Tid%22%3a%22066690f2-a8a6-4889-852e-124371dcbd6f%22%2c%22Oid%22%3a%22a343f6fd-86f8-4abe-95cf-3c7f4ad5f0ca%22%7d