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Abstract:
Since Lord Rayleigh conjectured that the disk should minimize the first Laplace-Dirichlet eigenvalue among all shapes of equal area more than a century ago, spectral study of elliptic operators has been active research topics with applications in various areas including mechanical vibration, optical resonator, photonic crystals, liquid sloshing, and population dynamics. This minisymposium features the latest progress on numerical and theoretical approaches for solving linear and nonlinear eigenvalue problems, eigenvalue optimization, and their applications.
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