Calculus of Variations and Geometric Measure Theory

F. Flei├čner

Minimal solutions to generalized $\Lambda$-semiflows and gradient flows in metric spaces

created by flei├čner on 22 Nov 2017
modified on 16 Sep 2022


Published Paper

Inserted: 22 nov 2017
Last Updated: 16 sep 2022

Journal: Annali di Matematica Pura ed Applicata
Year: 2022

ArXiv: 1711.07242 PDF


Generalized $\Lambda$-semiflows are an abstraction of semiflows with non-periodic solutions, for which there may be more than one solution corresponding to given initial data. A select class of solutions to generalized $\Lambda$-semiflows is introduced. It is proved that such minimal solutions are unique corresponding to given ranges and generate all other solutions by time reparametrization. Special qualities of minimal solutions are shown.

The concept of minimal solutions is applied to gradient flows in metric spaces and generalized semiflows. Generalized semiflows have been introduced by Ball.

Keywords: Gradient flows, Nonuniqueness, Generalized semiflows