The trace space of anisotropic least gradient functions depends on the anisotropy

We study the set of possible traces of anisotropic least gradient functions. We show that even on the unit disk it changes with the anisotropic norm: for two sufficiently regular strictly convex norms the trace spaces coincide if and only if the norms coincide. The example of a function in exactly o...

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Detalles Bibliográficos
Autor principal: Górny, Wojciech
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10587324/
https://www.ncbi.nlm.nih.gov/pubmed/37869580
http://dx.doi.org/10.1007/s00208-022-02488-4
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author Górny, Wojciech
author_facet Górny, Wojciech
author_sort Górny, Wojciech
collection PubMed
description We study the set of possible traces of anisotropic least gradient functions. We show that even on the unit disk it changes with the anisotropic norm: for two sufficiently regular strictly convex norms the trace spaces coincide if and only if the norms coincide. The example of a function in exactly one of the trace spaces is given by a characteristic function of a suitably chosen Cantor set.
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spelling pubmed-105873242023-10-21 The trace space of anisotropic least gradient functions depends on the anisotropy Górny, Wojciech Math Ann Article We study the set of possible traces of anisotropic least gradient functions. We show that even on the unit disk it changes with the anisotropic norm: for two sufficiently regular strictly convex norms the trace spaces coincide if and only if the norms coincide. The example of a function in exactly one of the trace spaces is given by a characteristic function of a suitably chosen Cantor set. Springer Berlin Heidelberg 2022-10-07 2023 /pmc/articles/PMC10587324/ /pubmed/37869580 http://dx.doi.org/10.1007/s00208-022-02488-4 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
Górny, Wojciech
The trace space of anisotropic least gradient functions depends on the anisotropy
title The trace space of anisotropic least gradient functions depends on the anisotropy
title_full The trace space of anisotropic least gradient functions depends on the anisotropy
title_fullStr The trace space of anisotropic least gradient functions depends on the anisotropy
title_full_unstemmed The trace space of anisotropic least gradient functions depends on the anisotropy
title_short The trace space of anisotropic least gradient functions depends on the anisotropy
title_sort trace space of anisotropic least gradient functions depends on the anisotropy
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10587324/
https://www.ncbi.nlm.nih.gov/pubmed/37869580
http://dx.doi.org/10.1007/s00208-022-02488-4
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