| Issue |
ESAIM: COCV
Volume 28, 2022
|
|
|---|---|---|
| Article Number | 59 | |
| Number of page(s) | 29 | |
| DOI | https://doi.org/10.1051/cocv/2022028 | |
| Published online | 18 August 2022 | |
A new minimizing-movements scheme for curves of maximal slope
1
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: ulisse.stefanelli@univie.ac.at
Received:
1
March
2021
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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