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
Article, Bibliographie
This is the latest version of this item.
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.
| Item Type: | Article |
|---|---|
| Erschienen: | 2021 |
| Creators: | Bechtel, Sebastian |
| Type of entry: | Bibliographie |
| Title: | The extension problem for fractional Sobolev spaces with a partial vanishing trace condition |
| Language: | English |
| Date: | 2021 |
| Place of Publication: | Berlin |
| Publisher: | Springer International Publishing |
| Journal or Publication Title: | Archiv der Mathematik |
| Volume of the journal: | 117 |
| Issue Number: | 1 |
| DOI: | 10.1007/s00013-021-01594-0 |
| Corresponding Links: | |
| 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. |
| Uncontrolled Keywords: | (Fractional) Sobolev spaces, Kondratiev spaces, Measure density condition, Extension operators, Hardy’s inequality |
| Classification DDC: | 500 Science and mathematics > 510 Mathematics |
| Divisions: | 04 Department of Mathematics 04 Department of Mathematics > Analysis |
| Date Deposited: | 05 Sep 2024 06:28 |
| Last Modified: | 05 Sep 2024 06:28 |
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| Suche nach Titel in: | TUfind oder in Google |
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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) [Currently Displayed]
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