A minimising movement scheme for the p-elastic energy of curves

We prove short-time existence for the negative [Formula: see text] -gradient flow of the p-elastic energy of curves via a minimising movement scheme. In order to account for the degeneracy caused by the energy’s invariance under curve reparametrisations, we write the evolving curves as approximate n...

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Detalles Bibliográficos
Autores principales: Blatt, Simon, Hopper, Christopher P., Vorderobermeier, Nicole
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9046362/
https://www.ncbi.nlm.nih.gov/pubmed/35535234
http://dx.doi.org/10.1007/s00028-022-00791-w
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author Blatt, Simon
Hopper, Christopher P.
Vorderobermeier, Nicole
author_facet Blatt, Simon
Hopper, Christopher P.
Vorderobermeier, Nicole
author_sort Blatt, Simon
collection PubMed
description We prove short-time existence for the negative [Formula: see text] -gradient flow of the p-elastic energy of curves via a minimising movement scheme. In order to account for the degeneracy caused by the energy’s invariance under curve reparametrisations, we write the evolving curves as approximate normal graphs over a fixed smooth curve. This enables us to establish short-time existence and give a lower bound on the solution’s lifetime that depends only on the [Formula: see text] -Sobolev norm of the initial data.
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spelling pubmed-90463622022-05-07 A minimising movement scheme for the p-elastic energy of curves Blatt, Simon Hopper, Christopher P. Vorderobermeier, Nicole J Evol Equ Article We prove short-time existence for the negative [Formula: see text] -gradient flow of the p-elastic energy of curves via a minimising movement scheme. In order to account for the degeneracy caused by the energy’s invariance under curve reparametrisations, we write the evolving curves as approximate normal graphs over a fixed smooth curve. This enables us to establish short-time existence and give a lower bound on the solution’s lifetime that depends only on the [Formula: see text] -Sobolev norm of the initial data. Springer International Publishing 2022-04-27 2022 /pmc/articles/PMC9046362/ /pubmed/35535234 http://dx.doi.org/10.1007/s00028-022-00791-w Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Blatt, Simon
Hopper, Christopher P.
Vorderobermeier, Nicole
A minimising movement scheme for the p-elastic energy of curves
title A minimising movement scheme for the p-elastic energy of curves
title_full A minimising movement scheme for the p-elastic energy of curves
title_fullStr A minimising movement scheme for the p-elastic energy of curves
title_full_unstemmed A minimising movement scheme for the p-elastic energy of curves
title_short A minimising movement scheme for the p-elastic energy of curves
title_sort minimising movement scheme for the p-elastic energy of curves
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9046362/
https://www.ncbi.nlm.nih.gov/pubmed/35535234
http://dx.doi.org/10.1007/s00028-022-00791-w
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