A stability estimate for a Cauchy problem for an elliptic partial differential equation
2005 (English)In: Inverse Problems, ISSN 0266-5611, Vol. 21, no 5, 1643-1653 p.Article in journal (Refereed) Published
A two-dimensional inverse steady state heat conduction problem in the unit square is considered. Cauchy data are given for y ≤ 0, and boundary data are for x ≤ 0 and x ≤ 1. The elliptic operator is self-adjoint with non-constant, smooth coefficients. The solution for y ≤ 1 is sought. This Cauchy problem is ill-posed in an L2-setting. A stability functional is defined, for which a differential inequality is derived. Using this inequality a stability result of Hölder type is proved. It is demonstrated explicitly how the stability depends on the smoothness of the coefficients. The results can also be used for rectangle-like regions that can be mapped conformally onto a rectangle. © 2005 IOP Publishing Ltd.
Place, publisher, year, edition, pages
2005. Vol. 21, no 5, 1643-1653 p.
Cauchy problem, elliptic equation, heat conduction, inverse problem
IdentifiersURN: urn:nbn:se:liu:diva-29345DOI: 10.1088/0266-5611/21/5/008Local ID: 14667OAI: oai:DiVA.org:liu-29345DiVA: diva2:250157