“Monotone vector fields in the Wasserstein space”
Venerdì 17 Maggio 2024, ore 11:15 - Aula 1BC50 - Nikolay Pogodaev (Università di Padova)
Abstract
The concept of a maximal monotone operator is well-known in the Hilbert setting, where such operators are closely related to partial differential equations that generate nonexpansive semigroups. In many cases, maximal monotone operators exhibit a gradient structure, implying that they can be represented as subdifferentials of proper convex lower semicontinuous functions. The corresponding partial differential equations are commonly referred to as gradient flows. The theory of gradient flows was extended from the Hilbert to the Wasserstein setting in the early 2000s. This extension was initiated in the papers of R. Jordan, D. Kinderlehrer, and F. Otto, and it reached its classical form in the monograph by L. Ambrosio, N. Gigli and G. Savarè, opening up numerous applications since then.
In the present talk, we explore the possibility of defining a monotone vector field in the Wasserstein space without necessarily adhering to a gradient form. We discuss the corresponding variant of the JKO scheme, provide examples of monotone vector fields, and explore potential applications.
