On the scattered field generated by a ball inhomogeneity of constant index (Q2891103)

In this article, the solution of the scalar Helmholtz equation in \(\mathbb{R}^2\) is considered. The potential (or index) takes two positive values, one inside a disk of radius \(\epsilon\) and another one outside. The author derives, for any frequencies and any contrast, sharp estimates of the size of the scattered field caused by such a disk inhomogeneity. Additionally, a uniform bound for the scattered field for any contrast and any frequencies outside of a set which tends to zero with \(\epsilon\) is provided.