EIGENVALUES OF MEMBRANES WITH REENTRANT CORNERS

In paper by L. Fox, P. Henrici and C. Moler bounds were obtained for first 10 eigenvalues of L-shaped membrane with fixed boundaries; method is here extended to find eigenvalues of H-shaped membrane, in which symmetries introduce some mixed boundary conditions into analysis; bounds for first six eigenvalues of H-shaped membrane are found, using inter-polation of boundary conditions at finite number of points, and effect of rounding on calculation of these bounds is considered; estimate of fundamental eigenvalue of H- membrane based on finite difference approximations.