Optimal Reconstruction of the Solution of the Dirichlet Problem from Inaccurate Input Data

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.