No Cover Image

Journal article 820 views 120 downloads

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

Check full text

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...

Full description

Published in: SIAM Journal on Mathematical Analysis
ISSN: 0036-1410 1095-7154
Published: Society for Industrial & Applied Mathematics (SIAM) 2016
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa28298
Tags: Add Tag
No Tags, Be the first to tag this record!
first_indexed 2016-05-25T03:17:21Z
last_indexed 2020-08-04T02:45:03Z
id cronfa28298
recordtype SURis
fullrecord <?xml version="1.0"?><rfc1807><datestamp>2020-08-03T13:16:54.6893126</datestamp><bib-version>v2</bib-version><id>28298</id><entry>2016-05-24</entry><title>A Regularity Result for the p-Laplacian Near Uniform Ellipticity</title><swanseaauthors><author><sid>46bf09624160610d6d6cf435996a5913</sid><ORCID>0000-0002-4289-5573</ORCID><firstname>Carlo</firstname><surname>Mercuri</surname><name>Carlo Mercuri</name><active>true</active><ethesisStudent>false</ethesisStudent></author></swanseaauthors><date>2016-05-24</date><deptcode>SMA</deptcode><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 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.</abstract><type>Journal Article</type><journal>SIAM Journal on Mathematical Analysis</journal><volume>48</volume><journalNumber>3</journalNumber><paginationStart>2059</paginationStart><paginationEnd>2075</paginationEnd><publisher>Society for Industrial &amp; Applied Mathematics (SIAM)</publisher><issnPrint>0036-1410</issnPrint><issnElectronic>1095-7154</issnElectronic><keywords>quasi-linear elliptic equations, regularity theory, degenerate elliptic equations</keywords><publishedDay>9</publishedDay><publishedMonth>6</publishedMonth><publishedYear>2016</publishedYear><publishedDate>2016-06-09</publishedDate><doi>10.1137/16m1058546</doi><url/><notes/><college>COLLEGE NANME</college><department>Mathematics</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>SMA</DepartmentCode><institution>Swansea University</institution><apcterm/><lastEdited>2020-08-03T13:16:54.6893126</lastEdited><Created>2016-05-24T18:20:41.6469445</Created><path><level id="1">College of Science</level><level id="2">Mathematics</level></path><authors><author><firstname>Carlo</firstname><surname>Mercuri</surname><orcid>0000-0002-4289-5573</orcid><order>1</order></author><author><firstname>Giuseppe</firstname><surname>Riey</surname><order>2</order></author><author><firstname>Berardino</firstname><surname>Sciunzi</surname><order>3</order></author></authors><documents><document><filename>0028298-24052016182639.pdf</filename><originalFilename>SiamMercuri.pdf</originalFilename><uploaded>2016-05-24T18:26:39.6370000</uploaded><type>Output</type><contentLength>347156</contentLength><contentType>application/pdf</contentType><version>Accepted Manuscript</version><cronfaStatus>true</cronfaStatus><embargoDate>2016-06-09T00:00:00.0000000</embargoDate><copyrightCorrect>true</copyrightCorrect><language>eng</language></document></documents><OutputDurs/></rfc1807>
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 SMA 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 COLLEGE CODE SMA Swansea University 2020-08-03T13:16:54.6893126 2016-05-24T18:20:41.6469445 College of 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 College of Science
hierarchytype
hierarchy_top_id collegeofscience
hierarchy_top_title College of Science
hierarchy_parent_id collegeofscience
hierarchy_parent_title College of Science
department_str Mathematics{{{_:::_}}}College of 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 2016-06-09T03:39:47Z
_version_ 1737025689574440960
score 10.89025