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URN to cite this document: urn:nbn:de:bvb:703-epub-9172-0
Title data
Frenkler, Joachim:
A mathematical foundation for QUMOND.
In: Journal of Mathematical Physics.
Vol. 66
(2025)
Issue 1
.
- 012501.
ISSN 1089-7658
DOI der Verlagsversion: https://doi.org/10.1063/5.0219100
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Project information
| Project title: |
Project's official title Project's id Mathematische Modellierung von Galaxien im Rahmen von MOND (Modified Newtonian Dynamics) 353124139 Open Access Publizieren No information |
|---|---|
| Project financing: |
Deutsche Forschungsgemeinschaft |
Abstract
We link the QUMOND theory with the Helmholtz-Weyl decomposition and introduce a new formula for the gradient of the Mondian potential using singular integral operators. This approach allows us to demonstrate that, under very general assumptions on the mass distribution, the Mondian potential is well-defined, once weakly differentiable, with its gradient given through the Helmholtz-Weyl decomposition. Furthermore, we establish that the gradient of the Mondian potential is an Lp vector field. These findings lay the foundation for a rigorous mathematical analysis of various issues within the realm of QUMOND. Further, we prove that the once weakly differentiable Mondian potential solves a second-order partial differential equation in distribution sense. Thus, the question arises whether the potential has second-order derivatives. We affirmatively answer this question in the situation of spherical symmetry, although our investigation reveals that the regularity of the second derivatives is weaker than anticipated. We doubt that a similarly general regularity result can be proven without symmetry assumptions. In conclusion, we explore the implications of our results for numerous problems within the domain of QUMOND.
Further data
| Item Type: | Article in a journal |
|---|---|
| Keywords: | General Relativity and Gravitation; Mathematics - Analysis of PDEs; Astrophysics - Astrophysics of Galaxies; Mathematical Physics |
| DDC Subjects: | 500 Science > 510 Mathematics 500 Science > 530 Physics |
| Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics VI (Nonlinear Analysis and Mathematical Physics) Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics |
| Language: | English |
| Originates at UBT: | Yes |
| URN: | urn:nbn:de:bvb:703-epub-9172-0 |
| Date Deposited: | 08 May 2026 12:09 |
| Last Modified: | 08 May 2026 12:09 |
| URI: | https://epub.uni-bayreuth.de/id/eprint/9172 |
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