We consider the stability issue for the inverse problem of determining an unknown portion Sigma of a two-dimensional simply connected domain from overdetermined boundary data for the Laplace equation. In this paper, we study the case in which Sigma is a polygonal line. We prove a Lipschitz stability estimate under further a priori geometric assumptions on Sigma.
Lipschitz stability for a stationary 2D inverse problem with unknown polygonal boundary / V. BACCHELLI; S. VESSELLA. - In: INVERSE PROBLEMS. - ISSN 0266-5611. - STAMPA. - 22:(2006), pp. 1627-1658. [10.1088/0266-5611/22/5/007]
Lipschitz stability for a stationary 2D inverse problem with unknown polygonal boundary
VESSELLA, SERGIO
2006
Abstract
We consider the stability issue for the inverse problem of determining an unknown portion Sigma of a two-dimensional simply connected domain from overdetermined boundary data for the Laplace equation. In this paper, we study the case in which Sigma is a polygonal line. We prove a Lipschitz stability estimate under further a priori geometric assumptions on Sigma.
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