No nonzero L2 solution of the Helmholtz equation exists in a 2D junction of three stratified half-planes with branch angles at least pi/2; hence no trapped modes there.
Bonnet-Ben Dhia, S
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A Rellich-type theorem for the Helmholtz equation in a junction of stratified media
No nonzero L2 solution of the Helmholtz equation exists in a 2D junction of three stratified half-planes with branch angles at least pi/2; hence no trapped modes there.