Optimal reconstruction of the solution of the Dirichlet problem from inaccurate input data. (English. Russian original) Zbl 1142.94316

Balova, E. A.

Math. Notes 82, No. 3, 285-294 (2007); translation from Mat. Zametki 82, No. 3, 323-334 (2007).

Summary: In this paper, we consider the optimal reconstruction of the solution of the Dirichlet problem in the \(d\)-dimensional ball on the sphere of radius \(r\) from inaccurately prescribed traces of the solution on the spheres of radii \(R_{1}\) and \(R_{2}\), where \(R_{1}<r<R_{2}\). We also study the optimal reconstruction of the solution of the Dirichlet problem in the \(d\)-dimensional ball from a finite collection of Fourier coefficients of the boundary function which are prescribed with an error in the mean-square and uniform metrics.

MSC:

94A12	Signal theory (characterization, reconstruction, filtering, etc.)
35J05	Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J25	Boundary value problems for second-order elliptic equations

Keywords:

Dirichlet problem; optimal reconstruction; inaccurate input data; Lagrange function; Beltrami-Laplace operator; Sobolev space

References:

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