TITLE

Sommerfeld condition for a Liouville equation and concentration of trajectories

AUTHOR(S)
Perthmae, Beno&icaron;t; Vega, Luis
PUB. DATE
April 2003
SOURCE
Bulletin of the Brazilian Mathematical Society;Apr2003, Vol. 34 Issue 1, p43
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We analyse the concentration of trajectories in a Liouville equation set in the full space with a potential which is not constant at infinity. Our motivation comes from geometrical optics where it appears as the high frequency limit of Helmholtz equation. We conjecture that the mass and energy concentrate on local maxima of the refraction index and prove a result in this direction. To do so, we establish a priori estimates in appropriate weighted spaces and various forms of a Sommerfeld radiation condition for solutions of such a stationary Liouville equation.
ACCESSION #
10616118

 

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