Regularity of solutions of elliptic problems with a curved fracture
We consider the Laplace equation with a right-hand side concentrated on a curved fracture of class Cm+2 for some nonnegative integer m (i.e., a sort of Dirac mass). We show that the solution belongs to a weighted Sobolev space of order m, the weight being the distance to this fracture. Our proof rel...
Gespeichert in:
| Veröffentlicht in: | Journal of mathematical analysis and applications 2017-03, Vol.447 (2), p.908-932 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 932 |
|---|---|
| container_issue | 2 |
| container_start_page | 908 |
| container_title | Journal of mathematical analysis and applications |
| container_volume | 447 |
| creator | Ariche, S. De Coster, C. Nicaise, S. |
| description | We consider the Laplace equation with a right-hand side concentrated on a curved fracture of class Cm+2 for some nonnegative integer m (i.e., a sort of Dirac mass). We show that the solution belongs to a weighted Sobolev space of order m, the weight being the distance to this fracture. Our proof relies on a priori estimates in a dihedron or a cone with singularities for elliptic operators with variable coefficients. In both cases, such an estimate is obtained using a dyadic covering of the domain. |
| doi_str_mv | 10.1016/j.jmaa.2016.10.021 |
| format | Article |
| fullrecord | <record><control><sourceid>elsevier_hal_p</sourceid><recordid>TN_cdi_hal_primary_oai_HAL_hal_03149894v1</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0022247X16306072</els_id><sourcerecordid>S0022247X16306072</sourcerecordid><originalsourceid>FETCH-LOGICAL-c334t-dbb36d5d6c6622ba61a7ca6ec7fa8ffd704e0454114267c6bfbb88b9f5cadd503</originalsourceid><addsrcrecordid>eNp9kE1Lw0AQhhdRsFb_gKe9ekjc2Ww2CXgpRa1QEETB27KfdkPalN1Npf_ehIpHTzPzMs_APAjdAsmBAL9v83YrZU7HfgxyQuEMzYA0PCM1FOdoRgilGWXV5yW6irElBKCsYIaWb_Zr6GTw6Yh7h2PfDcn3uzgNtuv8PnmN96FXnd1G_O3TBkush3CwBrsgdRqCvUYXTnbR3vzWOfp4enxfrrL16_PLcrHOdFGwlBmlCm5KwzXnlCrJQVZacqsrJ2vnTEWYJaxkAIzySnPllKpr1bhSS2NKUszR3enuRnZiH_xWhqPopRerxVpMGSmANXXDDjDu0tOuDn2Mwbo_AIiYlIlWTMrEpGzKRmUj9HCC7PjFwdsgovZ2p63xweokTO__w38A1p91iQ</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Regularity of solutions of elliptic problems with a curved fracture</title><source>Elsevier ScienceDirect Journals</source><source>EZB-FREE-00999 freely available EZB journals</source><creator>Ariche, S. ; De Coster, C. ; Nicaise, S.</creator><creatorcontrib>Ariche, S. ; De Coster, C. ; Nicaise, S.</creatorcontrib><description>We consider the Laplace equation with a right-hand side concentrated on a curved fracture of class Cm+2 for some nonnegative integer m (i.e., a sort of Dirac mass). We show that the solution belongs to a weighted Sobolev space of order m, the weight being the distance to this fracture. Our proof relies on a priori estimates in a dihedron or a cone with singularities for elliptic operators with variable coefficients. In both cases, such an estimate is obtained using a dyadic covering of the domain.</description><identifier>ISSN: 0022-247X</identifier><identifier>EISSN: 1096-0813</identifier><identifier>DOI: 10.1016/j.jmaa.2016.10.021</identifier><language>eng</language><publisher>Elsevier Inc</publisher><subject>Dirac measure ; Laplace equation ; Mathematics ; Regularity</subject><ispartof>Journal of mathematical analysis and applications, 2017-03, Vol.447 (2), p.908-932</ispartof><rights>2016 Elsevier Inc.</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c334t-dbb36d5d6c6622ba61a7ca6ec7fa8ffd704e0454114267c6bfbb88b9f5cadd503</citedby><cites>FETCH-LOGICAL-c334t-dbb36d5d6c6622ba61a7ca6ec7fa8ffd704e0454114267c6bfbb88b9f5cadd503</cites><orcidid>0000-0002-5230-7704 ; 0000-0003-3673-3495</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0022247X16306072$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>230,314,776,780,881,3537,27901,27902,65306</link.rule.ids><backlink>$$Uhttps://uphf.hal.science/hal-03149894$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Ariche, S.</creatorcontrib><creatorcontrib>De Coster, C.</creatorcontrib><creatorcontrib>Nicaise, S.</creatorcontrib><title>Regularity of solutions of elliptic problems with a curved fracture</title><title>Journal of mathematical analysis and applications</title><description>We consider the Laplace equation with a right-hand side concentrated on a curved fracture of class Cm+2 for some nonnegative integer m (i.e., a sort of Dirac mass). We show that the solution belongs to a weighted Sobolev space of order m, the weight being the distance to this fracture. Our proof relies on a priori estimates in a dihedron or a cone with singularities for elliptic operators with variable coefficients. In both cases, such an estimate is obtained using a dyadic covering of the domain.</description><subject>Dirac measure</subject><subject>Laplace equation</subject><subject>Mathematics</subject><subject>Regularity</subject><issn>0022-247X</issn><issn>1096-0813</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp9kE1Lw0AQhhdRsFb_gKe9ekjc2Ww2CXgpRa1QEETB27KfdkPalN1Npf_ehIpHTzPzMs_APAjdAsmBAL9v83YrZU7HfgxyQuEMzYA0PCM1FOdoRgilGWXV5yW6irElBKCsYIaWb_Zr6GTw6Yh7h2PfDcn3uzgNtuv8PnmN96FXnd1G_O3TBkush3CwBrsgdRqCvUYXTnbR3vzWOfp4enxfrrL16_PLcrHOdFGwlBmlCm5KwzXnlCrJQVZacqsrJ2vnTEWYJaxkAIzySnPllKpr1bhSS2NKUszR3enuRnZiH_xWhqPopRerxVpMGSmANXXDDjDu0tOuDn2Mwbo_AIiYlIlWTMrEpGzKRmUj9HCC7PjFwdsgovZ2p63xweokTO__w38A1p91iQ</recordid><startdate>20170315</startdate><enddate>20170315</enddate><creator>Ariche, S.</creator><creator>De Coster, C.</creator><creator>Nicaise, S.</creator><general>Elsevier Inc</general><general>Elsevier</general><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope><orcidid>https://orcid.org/0000-0002-5230-7704</orcidid><orcidid>https://orcid.org/0000-0003-3673-3495</orcidid></search><sort><creationdate>20170315</creationdate><title>Regularity of solutions of elliptic problems with a curved fracture</title><author>Ariche, S. ; De Coster, C. ; Nicaise, S.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c334t-dbb36d5d6c6622ba61a7ca6ec7fa8ffd704e0454114267c6bfbb88b9f5cadd503</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Dirac measure</topic><topic>Laplace equation</topic><topic>Mathematics</topic><topic>Regularity</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ariche, S.</creatorcontrib><creatorcontrib>De Coster, C.</creatorcontrib><creatorcontrib>Nicaise, S.</creatorcontrib><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>Journal of mathematical analysis and applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ariche, S.</au><au>De Coster, C.</au><au>Nicaise, S.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Regularity of solutions of elliptic problems with a curved fracture</atitle><jtitle>Journal of mathematical analysis and applications</jtitle><date>2017-03-15</date><risdate>2017</risdate><volume>447</volume><issue>2</issue><spage>908</spage><epage>932</epage><pages>908-932</pages><issn>0022-247X</issn><eissn>1096-0813</eissn><abstract>We consider the Laplace equation with a right-hand side concentrated on a curved fracture of class Cm+2 for some nonnegative integer m (i.e., a sort of Dirac mass). We show that the solution belongs to a weighted Sobolev space of order m, the weight being the distance to this fracture. Our proof relies on a priori estimates in a dihedron or a cone with singularities for elliptic operators with variable coefficients. In both cases, such an estimate is obtained using a dyadic covering of the domain.</abstract><pub>Elsevier Inc</pub><doi>10.1016/j.jmaa.2016.10.021</doi><tpages>25</tpages><orcidid>https://orcid.org/0000-0002-5230-7704</orcidid><orcidid>https://orcid.org/0000-0003-3673-3495</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0022-247X |
| ispartof | Journal of mathematical analysis and applications, 2017-03, Vol.447 (2), p.908-932 |
| issn | 0022-247X 1096-0813 |
| language | eng |
| recordid | cdi_hal_primary_oai_HAL_hal_03149894v1 |
| source | Elsevier ScienceDirect Journals; EZB-FREE-00999 freely available EZB journals |
| subjects | Dirac measure Laplace equation Mathematics Regularity |
| title | Regularity of solutions of elliptic problems with a curved fracture |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-05T12%3A39%3A51IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-elsevier_hal_p&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Regularity%20of%20solutions%20of%20elliptic%20problems%20with%20a%20curved%20fracture&rft.jtitle=Journal%20of%20mathematical%20analysis%20and%20applications&rft.au=Ariche,%20S.&rft.date=2017-03-15&rft.volume=447&rft.issue=2&rft.spage=908&rft.epage=932&rft.pages=908-932&rft.issn=0022-247X&rft.eissn=1096-0813&rft_id=info:doi/10.1016/j.jmaa.2016.10.021&rft_dat=%3Celsevier_hal_p%3ES0022247X16306072%3C/elsevier_hal_p%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rft_els_id=S0022247X16306072&rfr_iscdi=true |