×

zbMATH — the first resource for mathematics

On the reflection law for the Helmholtz equation. (English. Russian original) Zbl 0807.35024
Sov. Math., Dokl. 45, No. 1, 42-45 (1992); translation from Dokl. Akad. Nauk SSSR 322, No. 1, 48-51 (1992).
This article presents a new reflection formula for solutions to the two dimensional homogeneous Helmholtz equation. This formula connects values of the solution \(u(x,y)\) in domains \({\mathcal U}_ 1\) and \({\mathcal U}_ 2\) which are separated by a real analytic curve and is a generalization of the classical Schwartz symmetry principle.
Reviewer: P.Zabreiko (Minsk)

MSC:
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
PDF BibTeX XML Cite