Details
| Original language | English |
|---|---|
| Title of host publication | Modern Problems in PDEs and Applications |
| Subtitle of host publication | Extended Abstracts of the 2023 GAP Center Summer School |
| Publisher | Springer Science and Business Media Deutschland GmbH |
| Pages | 105-118 |
| Number of pages | 14 |
| ISBN (electronic) | 978-3-031-56732-2 |
| ISBN (print) | 978-3-031-56731-5 |
| Publication status | Published - 16 Jul 2024 |
Publication series
| Name | Trends in Mathematics |
|---|---|
| Volume | 4 |
| ISSN (Print) | 2297-0215 |
| ISSN (electronic) | 2297-024X |
Abstract
In these notes, I will recall the central elements of the cone calculus. The focus lies on conically degenerate differential operators and the Laplace-Beltrami operator with respect to a conically degenerate metric as a prototypical example. We will get to know manifolds with conical singularities, the Mellin transform, cone Sobolev spaces, and the notion of ellipticity in terms of the invertibility of the principal pseudodifferential symbol and the principal Mellin symbol. Finally, I will sketch the full cone calculus.
Keywords
- Cone calculus, Cone Sobolev spaces, Conical singularities, Conically degenerate operators
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
Cite this
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Modern Problems in PDEs and Applications: Extended Abstracts of the 2023 GAP Center Summer School. Springer Science and Business Media Deutschland GmbH, 2024. p. 105-118 (Trends in Mathematics; Vol. 4).
Research output: Chapter in book/report/conference proceeding › Contribution to book/anthology › Research › peer review
}
TY - CHAP
T1 - Introduction to the Analysis on Manifolds with Conical Singularities
AU - Schrohe, Elmar
N1 - Publisher Copyright: © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.
PY - 2024/7/16
Y1 - 2024/7/16
N2 - In these notes, I will recall the central elements of the cone calculus. The focus lies on conically degenerate differential operators and the Laplace-Beltrami operator with respect to a conically degenerate metric as a prototypical example. We will get to know manifolds with conical singularities, the Mellin transform, cone Sobolev spaces, and the notion of ellipticity in terms of the invertibility of the principal pseudodifferential symbol and the principal Mellin symbol. Finally, I will sketch the full cone calculus.
AB - In these notes, I will recall the central elements of the cone calculus. The focus lies on conically degenerate differential operators and the Laplace-Beltrami operator with respect to a conically degenerate metric as a prototypical example. We will get to know manifolds with conical singularities, the Mellin transform, cone Sobolev spaces, and the notion of ellipticity in terms of the invertibility of the principal pseudodifferential symbol and the principal Mellin symbol. Finally, I will sketch the full cone calculus.
KW - Cone calculus
KW - Cone Sobolev spaces
KW - Conical singularities
KW - Conically degenerate operators
UR - http://www.scopus.com/inward/record.url?scp=85200482516&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-56732-2_10
DO - 10.1007/978-3-031-56732-2_10
M3 - Contribution to book/anthology
AN - SCOPUS:85200482516
SN - 978-3-031-56731-5
T3 - Trends in Mathematics
SP - 105
EP - 118
BT - Modern Problems in PDEs and Applications
PB - Springer Science and Business Media Deutschland GmbH
ER -