Accepted Paper

Inserted: 15 apr 2025
Last Updated: 15 apr 2025

Year: 2025
Notes:

These are lecture notes for the courses which I gave in summer 2024 first in Rome (Vito Volterra meeting, June 20-24) and then in Chania (Festum Pi, July 8-12). They will be published in a Springer volume containing proceedings of the Chania event.

Abstract:

These lecture notes present the main results presented by the author in the courses he gave about the use of the Jordan-Kinderlehrer-Otto scheme in the approximation of the solutions of various linear or non-linear parabolic evolution equations with a gradient structure. The convergence of the scheme to a solution is proven, and estimates on the steps of the scheme are presented. Among the applications, BV and Sobolev bounds are detailed, a strategy to obtain functional inequalities is introduced, and a stronger convergence of the scheme to the solution of the PDE is proven.

Tags: EYAWKAJKOS

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