Volume 28, 2022
|Number of page(s)||29|
|Published online||18 August 2022|
A new minimizing-movements scheme for curves of maximal slope
Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria
2 Vienna Research Platform on Accelerating Photoreaction Discovery, University of Vienna, Währingerstraße 17, 1090 Wien, Austria
3 Istituto di Matematica Applicata e Tecnologie Informatiche E. Magenes, via Ferrata 1, 27100 Pavia, Italy
* Corresponding author: email@example.com
Accepted: 7 April 2022
Curves of maximal slope are a reference gradient-evolution notion in metric spaces and arise as variational formulation of a vast class of nonlinear diffusion equations. Existence theories for curves of maximal slope are often based on minimizing-movements schemes, most notably on the Euler scheme. We present here an alternative minimizing-movements approach, yielding more regular discretizations, serving as a-posteriori convergence estimator, and allowing for a simple convergence proof.
Mathematics Subject Classification: 35K55
Key words: Curves of maximal slope / minimizing movements / generalized geodesic convexity / nonlinear diffusion / Wasser stein spaces
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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