Böhnlein, Tim ; Egert, Moritz (2024)
Explicit improvements for Lp‐estimates related to elliptic systems.
In: Bulletin of the London Mathematical Society, 2024, 56 (3)
doi: 10.26083/tuprints-00027099
Article, Secondary publication, Publisher's Version
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Abstract
We give a simple argument to obtain Lp‐boundedness for heat semigroups associated to uniformly strongly elliptic systems on Rd by using Stein interpolation between Gaussian estimates and hypercontractivity. Our results give p explicitly in terms of ellipticity. It is optimal at the endpoint p = ∞. We also obtain Lp‐estimates for the gradient of the semigroup, where p > 2 depends on ellipticity but not on dimension.
| Item Type: | Article |
|---|---|
| Erschienen: | 2024 |
| Creators: | Böhnlein, Tim ; Egert, Moritz |
| Type of entry: | Secondary publication |
| Title: | Explicit improvements for Lp‐estimates related to elliptic systems |
| Language: | English |
| Date: | 18 June 2024 |
| Place of Publication: | Darmstadt |
| Year of primary publication: | March 2024 |
| Place of primary publication: | Hoboken |
| Publisher: | Wiley |
| Journal or Publication Title: | Bulletin of the London Mathematical Society |
| Volume of the journal: | 56 |
| Issue Number: | 3 |
| DOI: | 10.26083/tuprints-00027099 |
| URL / URN: | https://tuprints.ulb.tu-darmstadt.de/27099 |
| Corresponding Links: | |
| Origin: | Secondary publication DeepGreen |
| Abstract: | We give a simple argument to obtain Lp‐boundedness for heat semigroups associated to uniformly strongly elliptic systems on Rd by using Stein interpolation between Gaussian estimates and hypercontractivity. Our results give p explicitly in terms of ellipticity. It is optimal at the endpoint p = ∞. We also obtain Lp‐estimates for the gradient of the semigroup, where p > 2 depends on ellipticity but not on dimension. |
| Status: | Publisher's Version |
| URN: | urn:nbn:de:tuda-tuprints-270993 |
| Additional Information: | MSC 2020: 35J47, 47A60 (primary), 46B70 (secondary) |
| Classification DDC: | 500 Science and mathematics > 510 Mathematics |
| Divisions: | 04 Department of Mathematics 04 Department of Mathematics > Analysis |
| Date Deposited: | 18 Jun 2024 12:47 |
| Last Modified: | 20 Jun 2024 11:20 |
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| Suche nach Titel in: | TUfind oder in Google |
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