# Gradient flows in asymmetric metric spaces

Chenchiah, Isaac Vikram; Rieger, Marc Oliver; Zimmer, Johannes (2009). Gradient flows in asymmetric metric spaces. Nonlinear Analysis: Theory, Methods & Applications, 71(11):5820-5834.

## Abstract

This article is concerned with gradient flows in asymmetric metric spaces, that is, spaces with a topology induced by an asymmetric metric. Such an asymmetry appears naturally in many applications, e.g., in mathematical models for materials with hysteresis. A framework of asymmetric gradient flows is established under the assumption that the metric is weakly lower-semicontinuous in the second argument (and not necessarily on the first), and an existence theorem for gradient flows defined on an asymmetric metric space is given.

This article is concerned with gradient flows in asymmetric metric spaces, that is, spaces with a topology induced by an asymmetric metric. Such an asymmetry appears naturally in many applications, e.g., in mathematical models for materials with hysteresis. A framework of asymmetric gradient flows is established under the assumption that the metric is weakly lower-semicontinuous in the second argument (and not necessarily on the first), and an existence theorem for gradient flows defined on an asymmetric metric space is given.

## Citations

5 citations in Web of Science®
5 citations in Scopus®

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Item Type: Journal Article, refereed, original work 03 Faculty of Economics > Department of Banking and Finance 330 Economics English 1 December 2009 26 Feb 2010 15:40 05 Apr 2016 14:01 Elsevier 0362-546X https://doi.org/10.1016/j.na.2009.05.006 (Publisher)
Permanent URL: https://doi.org/10.5167/uzh-32445