Bechtel, Sebastian (2021)
The extension problem for fractional Sobolev spaces with a partial vanishing trace condition.
In: Archiv der Mathematik, 117 (1)
doi: 10.1007/s00013-021-01594-0
Artikel, Bibliographie
Dies ist die neueste Version dieses Eintrags.
Kurzbeschreibung (Abstract)
We construct whole-space extensions of functions in a fractional Sobolev space of order s ∈ (0, 1) and integrability p ∈ (0,∞) on an open set 0 which vanish in a suitable sense on a portion D of the boundary ∂O of 0. The set 0 is supposed to satisfy the so-called interior thickness condition in ∂O\D, which is much weaker than the global interior thickness condition. The proof works by means of a reduction to the case D = ∅ using a geometric construction.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2021 |
| Autor(en): | Bechtel, Sebastian |
| Art des Eintrags: | Bibliographie |
| Titel: | The extension problem for fractional Sobolev spaces with a partial vanishing trace condition |
| Sprache: | Englisch |
| Publikationsjahr: | 2021 |
| Ort: | Berlin |
| Verlag: | Springer International Publishing |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Archiv der Mathematik |
| Jahrgang/Volume einer Zeitschrift: | 117 |
| (Heft-)Nummer: | 1 |
| DOI: | 10.1007/s00013-021-01594-0 |
| Zugehörige Links: | |
| Kurzbeschreibung (Abstract): | We construct whole-space extensions of functions in a fractional Sobolev space of order s ∈ (0, 1) and integrability p ∈ (0,∞) on an open set 0 which vanish in a suitable sense on a portion D of the boundary ∂O of 0. The set 0 is supposed to satisfy the so-called interior thickness condition in ∂O\D, which is much weaker than the global interior thickness condition. The proof works by means of a reduction to the case D = ∅ using a geometric construction. |
| Freie Schlagworte: | (Fractional) Sobolev spaces, Kondratiev spaces, Measure density condition, Extension operators, Hardy’s inequality |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
| Fachbereich(e)/-gebiet(e): | 04 Fachbereich Mathematik 04 Fachbereich Mathematik > Analysis |
| Hinterlegungsdatum: | 05 Sep 2024 06:28 |
| Letzte Änderung: | 05 Sep 2024 06:28 |
| PPN: | |
| Export: | |
| Suche nach Titel in: | TUfind oder in Google |
Verfügbare Versionen dieses Eintrags
-
The extension problem for fractional Sobolev spaces with a partial vanishing trace condition. (deposited 03 Sep 2024 13:35)
- The extension problem for fractional Sobolev spaces with a partial vanishing trace condition. (deposited 05 Sep 2024 06:28) [Gegenwärtig angezeigt]
 |
Frage zum Eintrag |
Optionen (nur für Redakteure)
 |
Redaktionelle Details anzeigen |
Drucken
Impressum