Space-time integral currents of bounded variation

Author:

Rindler FilipORCID

Abstract

AbstractMotivated by a recent model for elasto-plastic evolutions that are driven by the flow of dislocations, this work develops a theory of space-time integral currents with bounded variation in time, which enables a natural variational approach to the analysis of rate-independent geometric evolutions. Based on this, we further introduce the notion of Lipschitz deformation distance between integral currents, which arises physically as a (simplified) dissipation distance. Several results are obtained: A Helly-type compactness theorem, a deformation theorem, an isoperimetric inequality, and the equivalence of the convergence in deformation distance with the classical notion of weak* (or flat) convergence. Finally, we prove that the Lipschitz deformation distance agrees with the (integral) homogeneous Whitney flat metric for boundaryless currents. Physically, this means that two seemingly different ways to measure the dissipation actually coincide.

Funder

European Research Council

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Analysis

Reference22 articles.

1. Abbaschian, R., Abbaschian, L., Reed-Hill, R.E.: Physical Metallurgy Principles—SI Edition. Cengage Learning, Boston (2009)

2. Oxford Mathematical Monographs;L Ambrosio,2000

3. Anderson, P.M., Hirth, J.P., Lothe, J.: Theory of Dislocations. Cambridge University Press, Cambridge (2017)

4. Brezis, H., Mironescu, P.: The Plateau problem from the perspective of optimal transport. C. R. Math. Acad. Sci. Paris 357, 597–612 (2019)

5. Chambolle, A., Ferrari, L.A.D., Merlet, B.: Strong approximation in $$h$$-mass of rectifiable currents under homological constraint. Adv. Calc. Var. 14, 343–363 (2021)

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. On the Transport of Currents;Milan Journal of Mathematics;2024-04-13

2. Existence and uniqueness for the transport of currents by Lipschitz vector fields;Journal of Functional Analysis;2024-04

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3