Geodesic
On the spectrum of the Laplacian with frequently alternating boundary conditions
Teoretičeskaâ i matematičeskaâ fizika, Tome 118 (1999) no. 3, pp. 347-353

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We consider a boundary problem for the Laplacian in a two-dimensional domain with frequently alternating boundary conditions. The leading terms of the asymptotic expansions of the eigenvalues and the corresponding eigenfunctions are constructed under the assumption that the limiting case is the mixed boundary problem. 
@article{TMF_1999_118_3_a3,
     author = {D. I. Borisov and R. R. Gadyl'shin},
     title = {On the spectrum of the {Laplacian} with frequently alternating boundary conditions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {347--353},
     publisher = {mathdoc},
     volume = {118},
     number = {3},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1999_118_3_a3/}
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D. I. Borisov; R. R. Gadyl'shin. On the spectrum of the Laplacian with frequently alternating boundary conditions. Teoretičeskaâ i matematičeskaâ fizika, Tome 118 (1999) no. 3, pp. 347-353. http://geodesic.mathdoc.fr/item/TMF_1999_118_3_a3/