An elliptic boundary problem acting on generalized Sobolev spaces

Denk, Robert; Faierman, Melvin

An elliptic boundary problem acting on generalized Sobolev spaces

Dateien

Denk_2-1u84ywg6aig2f7.pdfGröße: 358.19 KBDownloads: 128

Datum

2017

Autor:innen

Denk, Robert

Faierman, Melvin

Publikationstyp

Working Paper/Technical Report

Publikationsstatus

Published

Zusammenfassung

We consider an elliptic boundary problem over a bounded region Ω in Rⁿ and acting on the generalized Sobolev space W⁰,χ_p(Ω) for 1<p<∞. We note that similar problems for Ω either a bounded region in Rⁿ or a closed manifold acting on W⁰,χ₂(Ω), called H"{o}rmander space, have been the subject of investigation by various authors. Then in this paper we will, under the assumption of parameter-ellipticity, establish results pertaining to the existence and uniqueness of solutions of the boundary problem. Furthermore, under the further assumption that the boundary conditions are null, we will establish results pertaining to the spectral properties of the Banach space operator induced by the boundary problem, and in particular, to the angular and asymptotic distribution of its eigenvalues.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

Generalized Sobolev space, parameter-ellipticity, existence, uniqueness, eigenvalue asymptotics

Zitieren

ISO 690

DENK, Robert, Melvin FAIERMAN, 2017. An elliptic boundary problem acting on generalized Sobolev spaces

BibTex

@techreport{Denk2017-10-05T10:47:25Zellip-40438,
  year={2017},
  series={Konstanzer Schriften in Mathematik},
  title={An elliptic boundary problem acting on generalized Sobolev spaces},
  number={366},
  author={Denk, Robert and Faierman, Melvin}
}

RDF

<rdf:RDF
    xmlns:dcterms="http://purl.org/dc/terms/"
    xmlns:dc="http://purl.org/dc/elements/1.1/"
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:bibo="http://purl.org/ontology/bibo/"
    xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#"
    xmlns:foaf="http://xmlns.com/foaf/0.1/"
    xmlns:void="http://rdfs.org/ns/void#"
    xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > 
  <rdf:Description rdf:about="https://kops.uni-konstanz.de/server/rdf/resource/123456789/40438">
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2017-10-27T08:42:05Z</dc:date>
    <dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/40438/3/Denk_2-1u84ywg6aig2f7.pdf"/>
    <dc:contributor>Denk, Robert</dc:contributor>
    <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dc:creator>Denk, Robert</dc:creator>
    <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/40438"/>
    <dc:language>eng</dc:language>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dcterms:abstract xml:lang="eng">We consider an elliptic boundary problem over a bounded region Ω in R&lt;sup&gt;n&lt;/sup&gt; and acting on the generalized Sobolev space W&lt;sup&gt;0&lt;/sup&gt;,χ&lt;sub&gt;p&lt;/sub&gt;(Ω) for 1&lt;p&lt;∞. We note that similar problems for Ω either a bounded region in R&lt;sup&gt;n&lt;/sup&gt; or a closed manifold acting on W&lt;sup&gt;0&lt;/sup&gt;,χ&lt;sub&gt;2&lt;/sub&gt;(Ω), called H\"{o}rmander space, have been the subject of investigation by various authors. Then in this paper we will, under the assumption of parameter-ellipticity, establish results pertaining to the existence and uniqueness of solutions of the boundary problem. Furthermore, under the further assumption that the boundary conditions are null, we will establish results pertaining to the spectral properties of the Banach space operator induced by the boundary problem, and in particular, to the angular and asymptotic distribution of its eigenvalues.</dcterms:abstract>
    <dc:contributor>Faierman, Melvin</dc:contributor>
    <dc:creator>Faierman, Melvin</dc:creator>
    <dc:rights>terms-of-use</dc:rights>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <dcterms:title>An elliptic boundary problem acting on generalized Sobolev spaces</dcterms:title>
    <dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/40438/3/Denk_2-1u84ywg6aig2f7.pdf"/>
    <dcterms:issued>2017-10-05T10:47:25Z</dcterms:issued>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2017-10-27T08:42:05Z</dcterms:available>
  </rdf:Description>
</rdf:RDF>

Universitätsbibliographie

Ja