We consider an impedance boundary‐value problem for the Helmholtz equation which models a wave diffraction problem with imperfect conductivity on a union of strips. Pseudo‐differential operators acting between Bessel potential spaces and Besov spaces are used to deal with this wave diffraction problem. In particular, these operators allow a reformulation of the problem into a system of integral equations. The main result presents impedance parameters which ensure the well‐posedness of the problem in scales of Bessel potential spaces and Besov spaces.
Castro, L. P., & Kapanadze, D. (2008). Diffraction by a union of strips with impedance conditions in Besov and Bessel potential spaces. Mathematical Modelling and Analysis, 13(2), 183-194. https://doi.org/10.3846/1392-6292.2008.13.183-194
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