Least gradient problem via optimal transport

16.05.2022 14:20 - 15:05

Samer Dweik (Université de Versailles)

Abstract: In this talk, we show that the least gradient problem has an equivalent minimal flow formulation, which is in turn equivalent to an optimal transport problem. Thanks to this equivalence, we prove existence and uniqueness of a solution to the least gradient problem. Then, we study the summability of the transport density between two singular measures in the equivalent optimal transport formulation, which implies Sobolev regularity on the solution of the least gradient problem.


R. I. Boţ


HS 15, 2. OG, OMP 1