An iterative procedure for solving a Cauchy problem for second order elliptic equations

Tomas Johansson

Research output: Contribution to journalArticle

Abstract

An iterative method for reconstruction of solutions to second order elliptic equations by Cauchy data given on a part of the boundary, is presented. At each iteration step, a series of mixed well-posed boundary value problems are solved for the elliptic operator and its adjoint. The convergence proof of this method in a weighted L2 space is included. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Original languageEnglish
Pages (from-to)46-54
Number of pages9
JournalMathematische Nachrichten
Volume272
Issue number1
Early online date12 Jul 2004
DOIs
Publication statusPublished - Aug 2004

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Second Order Elliptic Equations
Iterative Procedure
Cauchy Problem
Iteration
Weighted Spaces
Elliptic Operator
Cauchy
Boundary Value Problem
Series

Keywords

  • cauchy problem
  • ill-posed
  • iterative method

Cite this

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An iterative procedure for solving a Cauchy problem for second order elliptic equations. / Johansson, Tomas.

In: Mathematische Nachrichten, Vol. 272, No. 1, 08.2004, p. 46-54.

Research output: Contribution to journalArticle

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