Completeness Theorems for Elliptic Equations of Higher Order with Constant Coefficients
Identifieur interne : 001847 ( Istex/Corpus ); précédent : 001846; suivant : 001848Completeness Theorems for Elliptic Equations of Higher Order with Constant Coefficients
Auteurs : Alberto CialdeaSource :
- Georgian Mathematical Journal [ 1072-947X ] ; 2007-03.
Abstract
Let {ω𝑘 } be a complete system of polynomial solutions of the elliptic equation ∑|α|⩽2𝑚 aα 𝐷 α 𝑢 = 0, aα being real constants. We give necessary and sufficient conditions for the completeness of the system in [𝐿𝑝(∂Ω)]𝑚, where Ω ⊂ is a bounded domain such that is connected and ∂Ω ∈ 𝐶1.
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DOI: 10.1515/GMJ.2007.81
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We give necessary and sufficient conditions for the completeness of the system in [𝐿𝑝(∂Ω)]𝑚, where Ω ⊂ is a bounded domain such that is connected and ∂Ω ∈ 𝐶1.</div></front></TEI><istex><corpusName>degruyter-journals</corpusName><author><json:item><name>Alberto Cialdea</name><affiliations><json:string>Dipartimento di Matematica, Università della Basilicata, Viale dell'Ateneo Lucano 10, 85100, Potenza, Italy. 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We give necessary and sufficient conditions for the completeness of the system in [𝐿𝑝(∂Ω)]𝑚, where Ω ⊂ is a bounded domain such that is connected and ∂Ω ∈ 𝐶1.</abstract><qualityIndicators><score>7.648</score><pdfVersion>1.2</pdfVersion><pdfPageSize>612 x 792 pts (letter)</pdfPageSize><refBibsNative>false</refBibsNative><keywordCount>3</keywordCount><abstractCharCount>293</abstractCharCount><pdfWordCount>5151</pdfWordCount><pdfCharCount>22465</pdfCharCount><pdfPageCount>17</pdfPageCount><abstractWordCount>54</abstractWordCount></qualityIndicators><title>Completeness Theorems for Elliptic Equations of Higher Order with Constant Coefficients</title><refBibs><json:item><author><json:item><name>A Cialdea</name></json:item></author><host><pages><last>32</last><first>34</first></pages><issue>2</issue><author></author><title>Rend. Circ. Mat. 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KG</publisher><availability><p>© Heldermann Verlag</p></availability><date>2010-03-10</date></publicationStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a" type="main" xml:lang="en">Completeness Theorems for Elliptic Equations of Higher Order with Constant Coefficients</title><author xml:id="author-1"><persName><forename type="first">Alberto</forename><surname>Cialdea</surname></persName><email>cialdea@email.it</email><email>cialdea@email.it</email></author></analytic><monogr><title level="j">Georgian Mathematical Journal</title><title level="j" type="abbrev">Georgian Mathematical Journal</title><idno type="pISSN">1072-947X</idno><idno type="eISSN">1072-9176</idno><imprint><publisher>Walter de Gruyter GmbH & Co. KG</publisher><date type="published" when="2007-03"></date><biblScope unit="volume">14</biblScope><biblScope unit="issue">1</biblScope><biblScope unit="page" from="81">81</biblScope><biblScope unit="page" to="97">97</biblScope></imprint></monogr><idno type="istex">6F5C5C0B54B4E5FC56D9C748ADC2A6FC7CB933FB</idno><idno type="DOI">10.1515/GMJ.2007.81</idno><idno type="ArticleID">GMJ.14.1.81</idno><idno type="pdf">gmj.2007.81.pdf</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>2010-03-10</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>Let {ω𝑘 } be a complete system of polynomial solutions of the elliptic equation ∑|α|⩽2𝑚 aα 𝐷 α 𝑢 = 0, aα being real constants. We give necessary and sufficient conditions for the completeness of the system in [𝐿𝑝(∂Ω)]𝑚, where Ω ⊂ is a bounded domain such that is connected and ∂Ω ∈ 𝐶1.</p></abstract><textClass><keywords scheme="keyword"><list><head>Key words and phrases</head><item><term>Completeness theorems</term></item><item><term>higher order elliptic equations</term></item><item><term>potential theory</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="2010-03-10">Created</change><change when="2007-03">Published</change><change xml:id="refBibs-istex" who="#ISTEX-API" when="2017-01-17">References added</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/6F5C5C0B54B4E5FC56D9C748ADC2A6FC7CB933FB/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="corpus degruyter-journals" wicri:toSee="no header"><istex:xmlDeclaration>version="1.0" encoding="UTF-8"</istex:xmlDeclaration><istex:docType PUBLIC="-//Atypon//DTD Atypon Systems Archival NLM DTD Suite v2.2.0 20090301//EN" URI="nlm-dtd/archivearticle.dtd" name="istex:docType"></istex:docType><istex:document><article article-type="research-article" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">GMJ</journal-id><abbrev-journal-title abbrev-type="full">Georgian Mathematical Journal</abbrev-journal-title><issn pub-type="ppub">1072-947X</issn><issn pub-type="epub">1072-9176</issn><publisher><publisher-name>Walter de Gruyter GmbH & Co. KG</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">GMJ.14.1.81</article-id><article-id pub-id-type="doi">10.1515/GMJ.2007.81</article-id><title-group><article-title>Completeness Theorems for Elliptic Equations of Higher Order with Constant Coefficients</article-title></title-group><contrib-group><contrib contrib-type="author"><name name-style="western"><given-names>Alberto</given-names><x> </x><surname>Cialdea</surname></name><xref ref-type="aff" rid="aff1"><sup>1</sup></xref></contrib><aff id="aff1"><sup>1</sup>Dipartimento di Matematica, Università della Basilicata, Viale dell'Ateneo Lucano 10, 85100, Potenza, Italy. E-mail: <email xlink:href="mailto:cialdea@email.it">cialdea@email.it</email></aff></contrib-group><pub-date pub-type="ppub"><month>March</month><year>2007</year></pub-date><pub-date pub-type="epub"><day>10</day><month>03</month><year>2010</year></pub-date><volume>14</volume><issue>1</issue><fpage>81</fpage><lpage>97</lpage><history><date date-type="received"><day>30</day><month>07</month><year>2006</year><string-date>Received 30.07.2006.</string-date></date></history><copyright-statement>© Heldermann Verlag</copyright-statement><related-article related-article-type="pdf" xlink:href="gmj.2007.81.pdf"></related-article><abstract><title>Abstract</title><p>Let {<italic>ω<sub>𝑘</sub></italic>} be a complete system of polynomial solutions of the elliptic equation ∑<sub>|<italic>α</italic>|⩽2𝑚</sub><italic>a<sub>α</sub></italic>𝐷<italic><sup>α</sup></italic>𝑢 = 0, <italic>a<sub>α</sub></italic> being real constants. We give necessary and sufficient conditions for the completeness of the system <inline-graphic xlink:href="gmj.2007.81_eq1.gif"></inline-graphic> in [𝐿<sup>𝑝</sup>(∂Ω)]<sup>𝑚</sup>, where Ω ⊂ <inline-graphic xlink:href="gmj.2007.81_eq3.gif"></inline-graphic> is a bounded domain such that <inline-graphic xlink:href="gmj.2007.81_eq2.gif"></inline-graphic> is connected and ∂Ω ∈ 𝐶<sup>1</sup>.</p></abstract><kwd-group><title>Key words and phrases:</title><kwd>Completeness theorems</kwd><x>, </x><kwd>higher order elliptic equations</kwd><x>, </x><kwd>potential theory</kwd><x>.</x></kwd-group></article-meta></front></article></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Completeness Theorems for Elliptic Equations of Higher Order with Constant Coefficients</title></titleInfo><titleInfo type="alternative" lang="en" contentType="CDATA"><title>Completeness Theorems for Elliptic Equations of Higher Order with Constant Coefficients</title></titleInfo><name type="personal"><namePart type="given">Alberto</namePart><namePart type="family">Cialdea</namePart><affiliation>Dipartimento di Matematica, Università della Basilicata, Viale dell'Ateneo Lucano 10, 85100, Potenza, Italy. E-mail: cialdea@email.it</affiliation><affiliation>E-mail: cialdea@email.it</affiliation></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="research-article"></genre><originInfo><publisher>Walter de Gruyter GmbH & Co. KG</publisher><dateIssued encoding="w3cdtf">2007-03</dateIssued><dateCreated encoding="w3cdtf">2010-03-10</dateCreated><copyrightDate encoding="w3cdtf">2007</copyrightDate></originInfo><language><languageTerm type="code" authority="iso639-2b">eng</languageTerm><languageTerm type="code" authority="rfc3066">en</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType></physicalDescription><abstract lang="en">Let {ω𝑘 } be a complete system of polynomial solutions of the elliptic equation ∑|α|⩽2𝑚 aα 𝐷 α 𝑢 = 0, aα being real constants. We give necessary and sufficient conditions for the completeness of the system in [𝐿𝑝(∂Ω)]𝑚, where Ω ⊂ is a bounded domain such that is connected and ∂Ω ∈ 𝐶1.</abstract><subject><genre>Key words and phrases</genre><topic>Completeness theorems</topic><topic>higher order elliptic equations</topic><topic>potential theory</topic></subject><relatedItem type="host"><titleInfo><title>Georgian Mathematical Journal</title></titleInfo><titleInfo type="abbreviated"><title>Georgian Mathematical Journal</title></titleInfo><genre type="journal">journal</genre><identifier type="ISSN">1072-947X</identifier><identifier type="eISSN">1072-9176</identifier><identifier type="PublisherID">GMJ</identifier><part><date>2007</date><detail type="volume"><caption>vol.</caption><number>14</number></detail><detail type="issue"><caption>no.</caption><number>1</number></detail><extent unit="pages"><start>81</start><end>97</end></extent></part></relatedItem><identifier type="istex">6F5C5C0B54B4E5FC56D9C748ADC2A6FC7CB933FB</identifier><identifier type="DOI">10.1515/GMJ.2007.81</identifier><identifier type="ArticleID">GMJ.14.1.81</identifier><identifier type="pdf">gmj.2007.81.pdf</identifier><accessCondition type="use and reproduction" contentType="copyright">© Heldermann Verlag</accessCondition><recordInfo><recordContentSource>De Gruyter</recordContentSource></recordInfo></mods></metadata><annexes><json:item><extension>gif</extension><original>true</original><mimetype>image/gif</mimetype><uri>https://api.istex.fr/document/6F5C5C0B54B4E5FC56D9C748ADC2A6FC7CB933FB/annexes/gif</uri></json:item></annexes><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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