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An extension problem related to the fractional Branson-Gover operators
Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review
Dokumenter
- 1904.03073v1
Anden version, 290 KB, PDF-dokument
DOI
- https://doi.org/10.1016/j.jfa.2019.108395
Forlagets udgivne version
- Jan Frahm
- Bent Ørsted
- Genkai Zhang, Chalmers University of Technology, University of Gothenburg, Sverige
The Branson-Gover operators are conformally invariant differential operators of even degree acting on differential forms. They can be interpolated by a holomorphic family of conformally invariant integral operators called fractional Branson-Gover operators. For Euclidean spaces we show that the fractional Branson-Gover operators can be obtained as Dirichlet-to-Neumann operators of certain conformally invariant boundary value problems, generalizing the work of Caffarelli-Silvestre for the fractional Laplacians to differential forms. The relevant boundary value problems are studied in detail and we find appropriate Sobolev type spaces in which there exist unique solutions and obtain the explicit integral kernels of the solution operators as well as some of its properties.
| Originalsprog | Engelsk |
|---|---|
| Artikelnummer | 108395 |
| Tidsskrift | Journal of Functional Analysis |
| Vol/bind | 278 |
| Nummer | 5 |
| ISSN | 0022-1236 |
| DOI | |
| Status | Udgivet - mar. 2020 |
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