Optimal Lp-Lq-regularity for parabolic problems with inhomogeneous boundary data

Denk, Robert; Hieber, Matthias; Prüss, Jan

Optimal Lp-Lq-regularity for parabolic problems with inhomogeneous boundary data

Dateien

preprint_205.pdfGröße: 339.45 KBDownloads: 397

Datum

2005

Autor:innen

Denk, Robert

Hieber, Matthias

Prüss, Jan

Publikationstyp

Preprint

Publikationsstatus

Published

Zusammenfassung

In this paper we investigate vector-valued parabolic initial boundary value problems (A(x,D), B1(x,D),..., Bm(x,D)) subject to general boundary conditions in a domain G with compact boundary. The top-order coefficients of the operator A are assumed to be continuous. We characterize optimal Lp-Lq-regularity for the solution of such problems in terms of the data. We also prove that the normal ellipticity condition on A and the Lopatinskii-Shapiro condition on (A(x,D), B1(x,D),..., Bm(x,D)) are necessary for these Lp-Lq-estimates. As a byproduct of the techniques being introduced we obtain new trace and extension results for Sobolev spaces of mixed order and a characterization of Triebel-Lizorkin spaces by boundary data.

Fachgebiet (DDC)

004 Informatik

Zitieren

ISO 690

DENK, Robert, Matthias HIEBER, Jan PRÜSS, 2005. Optimal Lp-Lq-regularity for parabolic problems with inhomogeneous boundary data

BibTex

@unpublished{Denk2005Optim-648,
  year={2005},
  title={Optimal Lp-Lq-regularity for parabolic problems with inhomogeneous boundary data},
  author={Denk, Robert and Hieber, Matthias and Prüss, Jan}
}

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/123456789/648">
    <dc:creator>Hieber, Matthias</dc:creator>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-03-22T17:45:22Z</dcterms:available>
    <dc:contributor>Prüss, Jan</dc:contributor>
    <dc:contributor>Hieber, Matthias</dc:contributor>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-03-22T17:45:22Z</dc:date>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <dc:creator>Denk, Robert</dc:creator>
    <dcterms:issued>2005</dcterms:issued>
    <dc:language>eng</dc:language>
    <bibo:uri rdf:resource="http://kops.uni-konstanz.de/handle/123456789/648"/>
    <dc:creator>Prüss, Jan</dc:creator>
    <dc:contributor>Denk, Robert</dc:contributor>
    <dc:rights>terms-of-use</dc:rights>
    <dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/648/1/preprint_205.pdf"/>
    <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/648/1/preprint_205.pdf"/>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dc:format>application/pdf</dc:format>
    <dcterms:title>Optimal Lp-Lq-regularity for parabolic problems with inhomogeneous boundary data</dcterms:title>
    <dcterms:abstract xml:lang="eng">In this paper we investigate vector-valued parabolic initial boundary value problems (A(x,D), B1(x,D),..., Bm(x,D)) subject to general boundary conditions in a domain G with compact boundary. The top-order coefficients of the operator A are assumed to be continuous. We characterize optimal Lp-Lq-regularity for the solution of such problems in terms of the data. We also prove that the normal ellipticity condition on A and the Lopatinskii-Shapiro condition on (A(x,D), B1(x,D),..., Bm(x,D)) are necessary for these Lp-Lq-estimates. As a byproduct of the techniques being introduced we obtain new trace and extension results for Sobolev spaces of mixed order and a characterization of Triebel-Lizorkin spaces by boundary data.</dcterms:abstract>
  </rdf:Description>
</rdf:RDF>

Universitätsbibliographie

Ja