Heat kernels and regularity for rough metrics on smooth manifolds
- We consider rough metrics on smooth manifolds and corresponding Laplacians induced by such metrics. We demonstrate that globally continuous heat kernels exist and are Holder continuous locally in space and time. This is done via local parabolic Harnack estimates for weak solutions of operators in divergence form with bounded measurable coefficients in weighted Sobolev spaces.
| Author details: | Lashi BandaraORCiD, Paul BryanORCiD |
|---|---|
| DOI: | https://doi.org/10.1002/mana.201800459 |
| ISSN: | 0025-584X |
| ISSN: | 1522-2616 |
| Title of parent work (English): | Mathematische Nachrichten |
| Publisher: | Wiley-VCH |
| Place of publishing: | Weinheim |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2020/09/28 |
| Publication year: | 2020 |
| Release date: | 2023/03/24 |
| Tag: | heat kernel; parabolic Harnack estimate; rough metrics |
| Volume: | 293 |
| Issue: | 12 |
| Number of pages: | 16 |
| First page: | 2255 |
| Last Page: | 2270 |
| Funding institution: | Knut & Alice Wallenberg Foundation; [KAW2013.0322]; German Research Foundation; (DFG); University of Queensland; EPSRCUK; Research & Innovation (UKRI) Engineering & Physical Sciences Research; Council (EPSRC) |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
| Publishing method: | Open Access |
