A new minimizing-movements scheme for curves of maximal slope

Ulisse Stefanelli

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arXiv · 2103.00846

A new minimizing-movements scheme for curves of maximal slope

Ulisse Stefanelli

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Abstract

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.

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Ulisse Stefanelli. 2021-03-01. A new minimizing-movements scheme for curves of maximal slope. https://arxiv.org/abs/2103.00846

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