Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4593088 | Journal of Functional Analysis | 2006 | 53 Pages |
Abstract
We study the high-frequency limit of the Helmholtz equation with variable refraction index and a source term concentrated near a p-dimensional affine subspace. Under some conditions, we first derive uniform estimates in Besov spaces for the solutions. Then, we prove that the semi-classical measure associated with these solutions satisfies the stationary Liouville equation with an explicit source term and has certain radiation property at infinity.
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Physical Sciences and Engineering
Mathematics
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