Minimizing movements along a sequence of functionals and curves of maximal slope

TL;DR

This paper demonstrates that a condition used to analyze limits of curves of maximal slope can also characterize minimizing movements along a sequence of functionals as curves of maximal slope of a limit functional.

Contribution

It extends the applicability of a known condition to characterize minimizing movements in the context of sequences of functionals.

Findings

The condition effectively characterizes the limit of minimizing movements.

Curves of maximal slope can be identified as limits of minimizing movements.

The approach unifies the analysis of sequences of functionals and their limit.

Abstract

We prove that a general condition introduced by Colombo and Gobbino to study limits of curves of maximal slope allows also to characterize minimizing movements along a sequence of functionals as curves of maximal slope of a limit functional.