A local regularization scheme of Cauchy problem for the Laplace equation on a doubly connected domain

Abstract

The Cauchy problem of the Laplace equation is investigated for both exact and perturbed data on a doubly connected domain, i.e., the numerical reconstruction of the function value and the normal derivative value on a part of the boundary from the knowledge of exact or noisy Cauchy data on the remaining and accessible boundary, which is completely different from the Cauchy problem on a simply connected bounded region.