## Thin-layer solutions of the Helmholtz equation.(English)Zbl 1478.78070

Summary: This paper gives a brief overview of some configurations in which high-frequency wave propagation modelled by Helmholtz equation gives rise to solutions that vary rapidly across thin layers. The configurations are grouped according to their mathematical structure and tractability and one of them concerns a famous open problem of mathematical physics.

### MSC:

 78M35 Asymptotic analysis in optics and electromagnetic theory 78A05 Geometric optics 78A45 Diffraction, scattering 78A40 Waves and radiation in optics and electromagnetic theory 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 35K10 Second-order parabolic equations
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### References:

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