We discuss the ill-posed Cauchy problem for elliptic equations, which is pervasive in inverse
boundary value problems modeled by elliptic equations. We provide essentially optimal …

The aim of this paper is to develop a functional-analytic framework for the construction of
level set methods, when applied to shape optimization and shape reconstruction problems …

In this paper, based on the conditional stability estimate for ill-posed inverse problems, we
propose a new strategy for a priori choice of regularizing parameters in Tikhonov's …

In this paper we study a class of inverse problems associated to elliptic boundary value
problems. More precisely, those inverse problems in which the role of the unknown is played …

In this paper, the highly ill posed Cauchy problem for the Laplace equation is transformed to
a classical moment problem whose numerical approximation can be achieved. Proofs on its …

This paper investigates the numerical computation of a Cauchy problem for Laplace's
equation which is a typical ill‐posed problem. By using Green's formula, the problem is …

The authors propose and analyze a well-posed numerical scheme for a type of ill-posed
elliptic Cauchy problem by using a constrained minimization approach combined with the …

In this paper, the spectral meshless radial point interpolation (SMRPI) technique is applied
to the Cauchy problems of two-dimensional elliptic PDEs in annulus domains. Unknown …

Abstract Recently, Akduman and Kress (2002 Inverse Problems 18 1659–72) proposed a
conformal map** technique for reconstructing the interior boundary curve of a two …

For the problem to determine the shape of a perfectly conducting inclusion within a
conducting homogeneous host medium from overdetermined Cauchy data on the …