Optimal Stable Approximation for the Cauchy Problem for Laplace Equation

Abstract EN

Cauchy problem for Laplace equation in a strip is considered.

The optimal error bounds between the exact solution and its regularized approximation are given, which depend on the noise level either in a Hölder continuous way or in a logarithmic continuous way.

We also provide two special regularization methods, that is, the generalized Tikhonov regularization and the generalized singular value decomposition, which realize the optimal error bounds.