An Introduction to Maximal Regularity for Parabolic Evolution Equations

Lade...
Vorschaubild
Dateien
Zu diesem Dokument gibt es keine Dateien.
Datum
2021
Autor:innen
Herausgeber:innen
Kontakt
ISSN der Zeitschrift
Electronic ISSN
ISBN
Bibliografische Daten
Verlag
Schriftenreihe
Auflagebezeichnung
URI (zitierfähiger Link)
ArXiv-ID
Internationale Patentnummer
Angaben zur Forschungsförderung
Projekt
Open Access-Veröffentlichung
Core Facility der Universität Konstanz
Gesperrt bis
Titel in einer weiteren Sprache
Forschungsvorhaben
Organisationseinheiten
Zeitschriftenheft
Publikationstyp
Beitrag zu einem Konferenzband
Publikationsstatus
Published
Erschienen in
KOIKE, Shigeaki, ed., Hideo KOZONO, ed., Takayoshi OGAWA, ed. and others. Nonlinear Partial Differential Equations for Future Applications. Singapore: Springer, 2021, pp. 1-70. ISSN 2194-1009. eISSN 2194-1017. ISBN 978-981-3348-21-9. Available under: doi: 10.1007/978-981-33-4822-6_1
Zusammenfassung

In this note, we give an introduction to the concept of maximal Lp-regularity as a method to solve nonlinear partial differential equations. We first define maximal regularity for autonomous and non-autonomous problems and describe the connection to Fourier multipliers and R-boundedness. The abstract results are applied to a large class of parabolic systems in the whole space and to general parabolic boundary value problems. For this, both the construction of solution operators for boundary value problems and a characterization of trace spaces of Sobolev spaces are discussed. For the nonlinear equation, we obtain local in time well-posedness in appropriately chosen Sobolev spaces. This manuscript is based on known results and consists of an extended version of lecture notes on this topic.

Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
510 Mathematik
Schlagwörter
Maximal regularity, Fourier multipliers, Parabolic boundary value problems, Quasilinear evolution equations
Konferenz
International workshop on Nonlinear Partial Differential Equations for Future Applications, PDEFA 2017, 2. Okt. 2017 - 6. Okt. 2017, Sendai, Japan
Rezension
undefined / . - undefined, undefined
Zitieren
ISO 690DENK, Robert, 2021. An Introduction to Maximal Regularity for Parabolic Evolution Equations. International workshop on Nonlinear Partial Differential Equations for Future Applications, PDEFA 2017. Sendai, Japan, 2. Okt. 2017 - 6. Okt. 2017. In: KOIKE, Shigeaki, ed., Hideo KOZONO, ed., Takayoshi OGAWA, ed. and others. Nonlinear Partial Differential Equations for Future Applications. Singapore: Springer, 2021, pp. 1-70. ISSN 2194-1009. eISSN 2194-1017. ISBN 978-981-3348-21-9. Available under: doi: 10.1007/978-981-33-4822-6_1
BibTex
@inproceedings{Denk2021Intro-55632,
  year={2021},
  doi={10.1007/978-981-33-4822-6_1},
  title={An Introduction to Maximal Regularity for Parabolic Evolution Equations},
  isbn={978-981-3348-21-9},
  issn={2194-1009},
  publisher={Springer},
  address={Singapore},
  booktitle={Nonlinear Partial Differential Equations for Future Applications},
  pages={1--70},
  editor={Koike, Shigeaki and Kozono, Hideo and Ogawa, Takayoshi},
  author={Denk, Robert}
}
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/123456789/55632">
    <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/>
    <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/55632"/>
    <dcterms:issued>2021</dcterms:issued>
    <dcterms:title>An Introduction to Maximal Regularity for Parabolic Evolution Equations</dcterms:title>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dc:rights>terms-of-use</dc:rights>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dc:contributor>Denk, Robert</dc:contributor>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2021-11-24T10:11:56Z</dc:date>
    <dc:language>eng</dc:language>
    <dcterms:abstract xml:lang="eng">In this note, we give an introduction to the concept of maximal L&lt;sup&gt;p&lt;/sup&gt;-regularity as a method to solve nonlinear partial differential equations. We first define maximal regularity for autonomous and non-autonomous problems and describe the connection to Fourier multipliers and R-boundedness. The abstract results are applied to a large class of parabolic systems in the whole space and to general parabolic boundary value problems. For this, both the construction of solution operators for boundary value problems and a characterization of trace spaces of Sobolev spaces are discussed. For the nonlinear equation, we obtain local in time well-posedness in appropriately chosen Sobolev spaces. This manuscript is based on known results and consists of an extended version of lecture notes on this topic.</dcterms:abstract>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2021-11-24T10:11:56Z</dcterms:available>
    <dc:creator>Denk, Robert</dc:creator>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
  </rdf:Description>
</rdf:RDF>
Interner Vermerk
xmlui.Submission.submit.DescribeStep.inputForms.label.kops_note_fromSubmitter
Kontakt
URL der Originalveröffentl.
Prüfdatum der URL
Prüfungsdatum der Dissertation
Finanzierungsart
Kommentar zur Publikation
Allianzlizenz
Corresponding Authors der Uni Konstanz vorhanden
Internationale Co-Autor:innen
Universitätsbibliographie
Ja
Begutachtet
Diese Publikation teilen