The Library
Space-time integral currents of bounded variation
Tools
Tools
Tools
Rindler, Filip (2022) Space-time integral currents of bounded variation. Calculus of Variations and Partial Differential Equations, 62 (2). 54. doi:10.1007/s00526-022-02332-2 ISSN 0944-2669.
|
PDF
WRAP-Space-time-integral-currents-of-bounded-variation-Rindler-2022.pdf - Published Version - Requires a PDF viewer. Available under License Creative Commons Attribution 4.0. Download (492Kb) | Preview |
|
![[img]](https://wrap.warwick.ac.uk/style/images/fileicons/application_pdf.png) |
PDF
WRAP-Space-time-integral-currents-of-bounded-variation-Rindler-2022.pdf - Accepted Version Embargoed item. Restricted access to Repository staff only - Requires a PDF viewer. Download (413Kb) |
Official URL: http://dx.doi.org/10.1007/s00526-022-02332-2
Abstract
Motivated 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.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics Q Science > QD Chemistry |
||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Calculus of variations, Functions of bounded variation, Integrals, Dislocations in crystals , Lipschitz spaces | ||||||
| Journal or Publication Title: | Calculus of Variations and Partial Differential Equations | ||||||
| Publisher: | Springer | ||||||
| ISSN: | 0944-2669 | ||||||
| Official Date: | 24 December 2022 | ||||||
| Dates: |
|
||||||
| Volume: | 62 | ||||||
| Number: | 2 | ||||||
| Article Number: | 54 | ||||||
| DOI: | 10.1007/s00526-022-02332-2 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||
| Date of first compliant deposit: | 5 October 2022 | ||||||
| Date of first compliant Open Access: | 1 February 2023 | ||||||
| RIOXX Funder/Project Grant: |
|
||||||
| Related URLs: |
Request changes or add full text files to a record
Repository staff actions (login required)
 |
View Item |
Downloads
Downloads per month over past year
