Duality of capacities and Sobolev extendability in the plane

We reveal relations between the duality of capacities and the duality between Sobolev extendability of Jordan domains in the plane, and explain how to read the curve conditions involved in the Sobolev extendability of Jordan domains via the duality of capacities. Finally as an application, we give a...

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Detalles Bibliográficos
Autor principal: Zhang, Yi Ru-Ya
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2021
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7932497/
https://www.ncbi.nlm.nih.gov/pubmed/33748677
http://dx.doi.org/10.1007/s40627-021-00063-2
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author Zhang, Yi Ru-Ya
author_facet Zhang, Yi Ru-Ya
author_sort Zhang, Yi Ru-Ya
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description We reveal relations between the duality of capacities and the duality between Sobolev extendability of Jordan domains in the plane, and explain how to read the curve conditions involved in the Sobolev extendability of Jordan domains via the duality of capacities. Finally as an application, we give an alternative proof of the necessary condition for a Jordan planar domain to be [Formula: see text] -extension domain when [Formula: see text] .
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spelling pubmed-79324972021-03-19 Duality of capacities and Sobolev extendability in the plane Zhang, Yi Ru-Ya Complex Analysis Synerg Research We reveal relations between the duality of capacities and the duality between Sobolev extendability of Jordan domains in the plane, and explain how to read the curve conditions involved in the Sobolev extendability of Jordan domains via the duality of capacities. Finally as an application, we give an alternative proof of the necessary condition for a Jordan planar domain to be [Formula: see text] -extension domain when [Formula: see text] . Springer International Publishing 2021-02-22 2021 /pmc/articles/PMC7932497/ /pubmed/33748677 http://dx.doi.org/10.1007/s40627-021-00063-2 Text en © The Author(s) 2021 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 Research
Zhang, Yi Ru-Ya
Duality of capacities and Sobolev extendability in the plane
title Duality of capacities and Sobolev extendability in the plane
title_full Duality of capacities and Sobolev extendability in the plane
title_fullStr Duality of capacities and Sobolev extendability in the plane
title_full_unstemmed Duality of capacities and Sobolev extendability in the plane
title_short Duality of capacities and Sobolev extendability in the plane
title_sort duality of capacities and sobolev extendability in the plane
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7932497/
https://www.ncbi.nlm.nih.gov/pubmed/33748677
http://dx.doi.org/10.1007/s40627-021-00063-2
work_keys_str_mv AT zhangyiruya dualityofcapacitiesandsobolevextendabilityintheplane

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