Optimal partial regularity of very weak solutions to nonhomogeneous A-harmonic systems

We study partial regularity of very weak solutions to some nonhomogeneous A-harmonic systems. To obtain the reverse Hölder inequality of the gradient of a very weak solution, we construct a suitable test function by Hodge decomposition. With the aid of Gehring’s lemma, we prove that these very weak...

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Detalles Bibliográficos
Autores principales: Zhao, Qing, Chen, Shuhong
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5243924/
https://www.ncbi.nlm.nih.gov/pubmed/28163548
http://dx.doi.org/10.1186/s13660-017-1297-z
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author Zhao, Qing
Chen, Shuhong
author_facet Zhao, Qing
Chen, Shuhong
author_sort Zhao, Qing
collection PubMed
description We study partial regularity of very weak solutions to some nonhomogeneous A-harmonic systems. To obtain the reverse Hölder inequality of the gradient of a very weak solution, we construct a suitable test function by Hodge decomposition. With the aid of Gehring’s lemma, we prove that these very weak solutions are weak solutions. Further, we show that these solutions are in fact optimal Hölder continuity based on A-harmonic approximation technique.
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spelling pubmed-52439242017-02-01 Optimal partial regularity of very weak solutions to nonhomogeneous A-harmonic systems Zhao, Qing Chen, Shuhong J Inequal Appl Research We study partial regularity of very weak solutions to some nonhomogeneous A-harmonic systems. To obtain the reverse Hölder inequality of the gradient of a very weak solution, we construct a suitable test function by Hodge decomposition. With the aid of Gehring’s lemma, we prove that these very weak solutions are weak solutions. Further, we show that these solutions are in fact optimal Hölder continuity based on A-harmonic approximation technique. Springer International Publishing 2017-01-18 2017 /pmc/articles/PMC5243924/ /pubmed/28163548 http://dx.doi.org/10.1186/s13660-017-1297-z Text en © The Author(s) 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Zhao, Qing
Chen, Shuhong
Optimal partial regularity of very weak solutions to nonhomogeneous A-harmonic systems
title Optimal partial regularity of very weak solutions to nonhomogeneous A-harmonic systems
title_full Optimal partial regularity of very weak solutions to nonhomogeneous A-harmonic systems
title_fullStr Optimal partial regularity of very weak solutions to nonhomogeneous A-harmonic systems
title_full_unstemmed Optimal partial regularity of very weak solutions to nonhomogeneous A-harmonic systems
title_short Optimal partial regularity of very weak solutions to nonhomogeneous A-harmonic systems
title_sort optimal partial regularity of very weak solutions to nonhomogeneous a-harmonic systems
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5243924/
https://www.ncbi.nlm.nih.gov/pubmed/28163548
http://dx.doi.org/10.1186/s13660-017-1297-z
work_keys_str_mv AT zhaoqing optimalpartialregularityofveryweaksolutionstononhomogeneousaharmonicsystems
AT chenshuhong optimalpartialregularityofveryweaksolutionstononhomogeneousaharmonicsystems

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