Geodesic
Spectral boundary value problems for the~Helmholtz equation with spectral parameter in~boundary conditions on a~non-smooth surface
Sbornik. Mathematics, Tome 190 (1999) no. 1, pp. 29-69

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The spectral properties of four problems for the Helmholtz equation with spectral parameter in boundary or transmission conditions on a closed Lipschitz surface $S$ are studied. These problems are related to the classical integral operators of potential type on $S$ for the Helmholtz equation. They have been studied before in the case when $S$ is infinitely smooth. It is shown that the most important properties of eigenvalues and root functions hold also for Lipschitz surfaces $S$. The machinery of potential theory in Lipschitz domains and of spectral theory is used in the proofs. 
@article{SM_1999_190_1_a1,
     author = {M. S. Agranovich and R. Mennicken},
     title = {Spectral boundary value problems for {the~Helmholtz} equation with spectral parameter in~boundary conditions on a~non-smooth surface},
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     publisher = {mathdoc},
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     year = {1999},
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     url = {http://geodesic.mathdoc.fr/item/SM_1999_190_1_a1/}
}
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M. S. Agranovich; R. Mennicken. Spectral boundary value problems for the~Helmholtz equation with spectral parameter in~boundary conditions on a~non-smooth surface. Sbornik. Mathematics, Tome 190 (1999) no. 1, pp. 29-69. http://geodesic.mathdoc.fr/item/SM_1999_190_1_a1/