Liouville's equation: Difference between revisions
From DispersiveWiki
Jump to navigationJump to search
(New page: ''Liouville's equation''' <center><math>\Box u = \exp(u)</math></center> in <math>R^{1+1}</math> first arose in the problem of prescribing scalar curvature on a surface. It can be expli...) |
No edit summary |
||
| Line 1: | Line 1: | ||
''Liouville's equation''' | '''Liouville's equation''' | ||
<center><math>\Box u = \exp(u)</math></center> | <center><math>\Box u = \exp(u)</math></center> | ||
| Line 12: | Line 12: | ||
Standard energy methods give GWP in H^1. | Standard energy methods give GWP in H^1. | ||
== See also == | |||
* [http://en.wikipedia.org/wiki/Liouville%27s_equation] | |||
* [http://terrytao.wordpress.com/2009/01/22/an-explicitly-solvable-nonlinear-wave-equation] | |||
== References == | |||
# J. Liouville, Sur l'equation aux differences partielles <math>\partial^2 \ln \lambda /\partial u \partial v \pm 2 \lambda q^2=0</math>, J. Math. Pure Appl. 18(1853), 71--74. | # J. Liouville, Sur l'equation aux differences partielles <math>\partial^2 \ln \lambda /\partial u \partial v \pm 2 \lambda q^2=0</math>, J. Math. Pure Appl. 18(1853), 71--74. | ||
[[Category:Integrability]] | [[Category:Integrability]] | ||
[[Category:wave]] | [[Category:wave]] | ||
[[Category:Equations]] | [[Category:Equations]] | ||
Revision as of 23:46, 22 January 2009
Liouville's equation
in first arose in the problem of prescribing scalar curvature on a surface. It can be explicitly solved as
as was first observed by Liouville.
It is a limiting case of the sinh-gordon equation.
Standard energy methods give GWP in H^1.
See also
References
- J. Liouville, Sur l'equation aux differences partielles , J. Math. Pure Appl. 18(1853), 71--74.
