Recovery of a solution to the Dirichlet problem from incomplete initial data. (Russian) Zbl 1113.35313

Summary: The problem is under study of optimal recovery of a solution to the Dirichlet problem in the case when the information about boundary values of the solution is given as a finite set of its Fourier coefficients calculated with a prescribed accuracy in the mean-square or uniform norm.


35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series
41A25 Rate of convergence, degree of approximation
49N30 Problems with incomplete information (optimization)
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