Geodesic
Exitation of the wave field in the triangular domain with impedance boundary conditions
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 27, Tome 250 (1998), pp. 300-318

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The equation of Helmholtz in a close domain which is an equilateral triangle with nonhomogeneous impedance boundary conditions is considered. The functional equation in which an unknown function is Fourier-image of the wave field on the boundary of the domain is constracted. This functional equation is solved for the case of the homogeneous boundary conditions (the problem on eigenvalues) as well as for the case of the nonhomogeneous boundary conditions in the absence of the resonance. 
@article{ZNSL_1998_250_a19,
     author = {A. V. Shanin},
     title = {Exitation of the wave field in the triangular domain with impedance boundary conditions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {300--318},
     publisher = {mathdoc},
     volume = {250},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1998_250_a19/}
}
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A. V. Shanin. Exitation of the wave field in the triangular domain with impedance boundary conditions. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 27, Tome 250 (1998), pp. 300-318. http://geodesic.mathdoc.fr/item/ZNSL_1998_250_a19/