Methods of Mathematical Physics
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Asgeirsson's theorem implies that specifying u in a cylinder determines u throughout the region made up of truncated double cones.
“A corollary of a remarkable theorem by Asgeirsson [13] is that if we specify u in the cylinder in figure 3, then this determines u throughout the region made up of the truncated double cones.”
From On the dimensionality of spacetime (1997) · cites this paper as [13]
Asgeirsson's theorem also applies to the ultrahyperbolic case, showing that initial data on a hypersurface containing both space-like and time-like directions leads to an ill-posed problem.
“Asgeirsson's theorem also applies to the ultrahyperbolic case as well, showing that initial data on a hypersurface containing both space-like and time-like directions leads to an ill-posed problem.”
From On the dimensionality of spacetime (1997) · cites this paper as [13]
Cited by
Sorted by citations
The back reaction effect in particle creation in curved spacetime
Wald, R. M. (1977) · Communications in Mathematical Physics · doi:10.1007/bf01609833 · Cited by 317 · see citing works
On the dimensionality of spacetime
Tegmark, M. (1997) · Classical and Quantum Gravity · doi:10.1088/0264-9381/14/4/002 · Cited by 135 · see citing works
Causality and hyperbolicity of Lovelock theories
Reall, H. S., Tanahashi, N., & Way, B. (2014) · Classical and Quantum Gravity · doi:10.1088/0264-9381/31/20/205005 · Cited by 92 · see citing works
On determinism and well-posedness in multiple time dimensions
Craig, W., & Weinstein, S. (2009) · Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences · doi:10.1098/rspa.2009.0097 · Cited by 62 · see citing works
- Authors
- Courant, R., Hilbert, D., & Teichmann, T.
- Affiliations
- General Dynamics (United States) (US)
- Venue
- Physics Today
- Publisher
- AIP Publishing
- Published
- 1962-11-01
- Volume
- 15
- Issue
- 11
- Pages
- 62-63
- ISSN
- 0031-9228 (ISSN-L)
- 1945-0699
- OpenAlex
- W3022664448
- Cited by
- 1,419
- References
- 0
- Citations by year
- 2026: 5 · 2025: 14 · 2024: 9 · 2023: 12 · 2022: 4 · 2021: 20 · 2020: 10 · 2019: 18 · 2018: 25 · 2017: 20 · 2016: 30 · 2015: 22 · 2014: 18 · 2013: 26 · 2012: 31
- Type
- book review
- Language
- en
- Open access
- closed
- Locations
- Physics Today (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Applied Mathematics › Differential Equations and Boundary Problems
- Physical Sciences › Mathematics › Modeling and Simulation › Mathematical and Computational Methods
- Physical Sciences › Mathematics › Mathematical Physics › Spectral Theory in Mathematical Physics
- Keywords
- mathematical methods in physics, mathematical physics
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