On the scattered field generated by a ball inhomogeneity of constant index

Details On the scattered field generated by a ball inhomogeneity of constant index On the scattered field generated by a ball inhomogeneity of constant index

2011-08-02

arxiv.org/abs/1108.0615v2

Mathematics

Classical Analysis and ODEs

37 pages, 3 figures

Scientific paper

We consider the solution of a scalar Helmholtz equation where the potential (or index) takes two positive values, one inside a disk of radius $\epsilon$ and another one outside. We derive sharp estimates of the size of the scattered field caused by this disk inhomogeneity, for any frequencies and any contrast. We also provide a broadband estimate, that is, a uniform bound for the scattered field for any contrast, and any frequencies outside of a set which tend to zero with $\epsilon$.

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