Publikation:

Convex monotone semigroups on lattices of continuous functions

Lade...
Vorschaubild

Dateien

Zu diesem Dokument gibt es keine Dateien.

Datum

2021

Herausgeber:innen

Kontakt

ISSN der Zeitschrift

Electronic ISSN

ISBN

Bibliografische Daten

Verlag

Schriftenreihe

Auflagebezeichnung

URI (zitierfähiger Link)
DOI (zitierfähiger Link)

Internationale Patentnummer

Angaben zur Forschungsförderung

Projekt

Open Access-Veröffentlichung
Core Facility der Universität Konstanz

Gesperrt bis

Titel in einer weiteren Sprache

Publikationstyp
Preprint
Publikationsstatus
Published

Erschienen in

Zusammenfassung

We consider convex monotone C0-semigroups on a Banach lattice, which is assumed to be a Riesz subspace of a σ-Dedekind complete Banach lattice. Typical examples include the space of all bounded uniformly continuous functions and the space of all continuous functions vanishing at infinity. We show that the domain of the classical generator of a convex semigroup is typically not invariant. Therefore, we propose alternative versions for the domain, such as the monotone domain and the Lipschitz set, for which we prove invariance under the semigroup. As a main result, we obtain the uniqueness of the semigroup in terms of an extended version of the generator. The results are illustrated with several examples related to Hamilton-Jacobi-Bellman equations, including nonlinear versions of the shift semigroup and the heat equation. In particular, we determine their symmetric Lipschitz sets, which are invariant and allow to understand the generators in a weak sense.

Zusammenfassung in einer weiteren Sprache

Fachgebiet (DDC)
510 Mathematik

Schlagwörter

Konferenz

Rezension
undefined / . - undefined, undefined

Forschungsvorhaben

Organisationseinheiten

Zeitschriftenheft

Zugehörige Datensätze in KOPS

Zitieren

ISO 690DENK, Robert, Michael KUPPER, Max NENDEL, 2021. Convex monotone semigroups on lattices of continuous functions
BibTex
@unpublished{Denk2021Conve-55474,
  year={2021},
  title={Convex monotone semigroups on lattices of continuous functions},
  author={Denk, Robert and Kupper, Michael and Nendel, Max}
}
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/123456789/55474">
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2021-11-08T13:51:05Z</dc:date>
    <dc:language>eng</dc:language>
    <dcterms:issued>2021</dcterms:issued>
    <dc:creator>Kupper, Michael</dc:creator>
    <dc:creator>Nendel, Max</dc:creator>
    <dc:contributor>Denk, Robert</dc:contributor>
    <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/55474"/>
    <dc:rights>terms-of-use</dc:rights>
    <dcterms:abstract xml:lang="eng">We consider convex monotone C&lt;sub&gt;0&lt;/sub&gt;-semigroups on a Banach lattice, which is assumed to be a Riesz subspace of a σ-Dedekind complete Banach lattice. Typical examples include the space of all bounded uniformly continuous functions and the space of all continuous functions vanishing at infinity. We show that the domain of the classical generator of a convex semigroup is typically not invariant. Therefore, we propose alternative versions for the domain, such as the monotone domain and the Lipschitz set, for which we prove invariance under the semigroup. As a main result, we obtain the uniqueness of the semigroup in terms of an extended version of the generator. The results are illustrated with several examples related to Hamilton-Jacobi-Bellman equations, including nonlinear versions of the shift semigroup and the heat equation. In particular, we determine their symmetric Lipschitz sets, which are invariant and allow to understand the generators in a weak sense.</dcterms:abstract>
    <dc:contributor>Nendel, Max</dc:contributor>
    <dcterms:title>Convex monotone semigroups on lattices of continuous functions</dcterms:title>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2021-11-08T13:51:05Z</dcterms:available>
    <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dc:contributor>Kupper, Michael</dc:contributor>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <dc:creator>Denk, Robert</dc:creator>
    <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"/>
  </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