Revisiting Fortet's proof of existence of a solution to the Schrödinger system

Abstract

Since a few years, the Schrödinger problem captures the attention of a growing community of mathematicians interested in optimal transport problems. The first result of existence of a solution to this problem dates back to 1940, when Fortet published an article on the subject. In these notes, Fortet's original proof of existence and uniqueness of a solution to the Schrödinger system is revisited.

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