Existence and uniqueness of scattering solutions in non-smooth domains

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Abstract

A short and self-contained proof of the existence of the scattering solution in exterior domains is presented for some class of second order elliptic equations. The method does not use the integral equation; it is based on Fredholm theory and the limiting absorption principle for solutions in the whole space. It covers domains with Lipschitz boundaries, domains satisfying a cone condition, and those with the so-called local compactness property. © 1996 Academic Press, Inc.

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Ramm, A. G., & Ruiz, A. (1996). Existence and uniqueness of scattering solutions in non-smooth domains. Journal of Mathematical Analysis and Applications, 201(2), 329–338. https://doi.org/10.1006/jmaa.1996.0258

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