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A stability estimate for a Cauchy problem for an elliptic partial differential equation
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Scientific Computing.ORCID iD: 0000-0003-2281-856X
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Scientific Computing.
2005 (English)In: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 21, no 5, 1643-1653 p.Article in journal (Refereed) Published
Abstract [en]

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.
Keyword [en]
Cauchy problem, elliptic equation, heat conduction, inverse problem
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-29345DOI: 10.1088/0266-5611/21/5/008Local ID: 14667OAI: oai:DiVA.org:liu-29345DiVA: diva2:250157
Available from: 2009-10-09 Created: 2009-10-09 Last updated: 2017-12-13

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Publisher's full texthttp://www.iop.org/EJ/abstract/0266-5611/21/5/008/

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Elden, LarsBerntsson, Fredrik

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