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Isospectral domains with mixed boundary conditions. (English) Zbl 1089.58021

Summary: We construct a series of examples of planar isospectral domains with mixed Dirichlet-Neumann boundary conditions. This is a modification of a classical problem proposed by M. Kac.

MSC:

58J53 Isospectrality
35P05 General topics in linear spectral theory for PDEs