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A Regularity Result for the p-Laplacian Near Uniform Ellipticity

Carlo Mercuri Orcid Logo, Giuseppe Riey, Berardino Sciunzi

SIAM Journal on Mathematical Analysis, Volume: 48, Issue: 3, Pages: 2059 - 2075

Swansea University Author: Carlo Mercuri Orcid Logo

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DOI (Published version): 10.1137/16m1058546

Abstract

We consider weak solutions to a class of Dirichlet boundary value problems involving the $p$-Laplace operator, and prove that the second weak derivatives have summability as high as it is desirable, provided p is sufficiently close to 2. And as a consequence the Holder exponent of the gradients appr...

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Published in: SIAM Journal on Mathematical Analysis
ISSN: 0036-1410 1095-7154
Published: Society for Industrial & Applied Mathematics (SIAM) 2016
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URI: https://cronfa.swan.ac.uk/Record/cronfa28298
first_indexed 2016-05-25T03:17:21Z
last_indexed 2020-08-04T02:45:03Z
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spelling 2020-08-03T13:16:54.6893126 v2 28298 2016-05-24 A Regularity Result for the p-Laplacian Near Uniform Ellipticity 46bf09624160610d6d6cf435996a5913 0000-0002-4289-5573 Carlo Mercuri Carlo Mercuri true false 2016-05-24 MACS We consider weak solutions to a class of Dirichlet boundary value problems involving the $p$-Laplace operator, and prove that the second weak derivatives have summability as high as it is desirable, provided p is sufficiently close to 2. And as a consequence the Holder exponent of the gradients approaches 1. We show that this phenomenon is driven by the classical Calderon-Zygmund constant. We believe that this result is particularly interesting in higher dimensions, and it is related to the optimal regularity of $p$-harmonic mappings. which is still an open question. Journal Article SIAM Journal on Mathematical Analysis 48 3 2059 2075 Society for Industrial & Applied Mathematics (SIAM) 0036-1410 1095-7154 quasi-linear elliptic equations, regularity theory, degenerate elliptic equations 9 6 2016 2016-06-09 10.1137/16m1058546 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University 2020-08-03T13:16:54.6893126 2016-05-24T18:20:41.6469445 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Carlo Mercuri 0000-0002-4289-5573 1 Giuseppe Riey 2 Berardino Sciunzi 3 0028298-24052016182639.pdf SiamMercuri.pdf 2016-05-24T18:26:39.6370000 Output 347156 application/pdf Accepted Manuscript true 2016-06-09T00:00:00.0000000 true eng
title A Regularity Result for the p-Laplacian Near Uniform Ellipticity
spellingShingle A Regularity Result for the p-Laplacian Near Uniform Ellipticity
Carlo Mercuri
title_short A Regularity Result for the p-Laplacian Near Uniform Ellipticity
title_full A Regularity Result for the p-Laplacian Near Uniform Ellipticity
title_fullStr A Regularity Result for the p-Laplacian Near Uniform Ellipticity
title_full_unstemmed A Regularity Result for the p-Laplacian Near Uniform Ellipticity
title_sort A Regularity Result for the p-Laplacian Near Uniform Ellipticity
author_id_str_mv 46bf09624160610d6d6cf435996a5913
author_id_fullname_str_mv 46bf09624160610d6d6cf435996a5913_***_Carlo Mercuri
author Carlo Mercuri
author2 Carlo Mercuri
Giuseppe Riey
Berardino Sciunzi
format Journal article
container_title SIAM Journal on Mathematical Analysis
container_volume 48
container_issue 3
container_start_page 2059
publishDate 2016
institution Swansea University
issn 0036-1410
1095-7154
doi_str_mv 10.1137/16m1058546
publisher Society for Industrial & Applied Mathematics (SIAM)
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description We consider weak solutions to a class of Dirichlet boundary value problems involving the $p$-Laplace operator, and prove that the second weak derivatives have summability as high as it is desirable, provided p is sufficiently close to 2. And as a consequence the Holder exponent of the gradients approaches 1. We show that this phenomenon is driven by the classical Calderon-Zygmund constant. We believe that this result is particularly interesting in higher dimensions, and it is related to the optimal regularity of $p$-harmonic mappings. which is still an open question.
published_date 2016-06-09T03:51:30Z
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score 11.089738

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