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VIDEO LIBRARY |
Spectral theory, nonlinear problems, and applications
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Spectral problem of Poincaré and Steklov A. B. Bogatyrev |
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Abstract: We consider a spectral problem with a pair of boundary influence operators (transforming the Dirichlet data of a harmonic function into its Neumann data) for a pair of planar domains with a common boundary. Similar problems arise when we justify and optimize the computational methods such as domain decomposition and fictitious domains. The problem reduces to studying a pencil of one-dimensional integral operators with Cauchy and Grunsky kernels. The possibility of finding the eigenvalues and functions of the simplest pencils in a closed analytical form is investigated. |