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An iterative procedure for solving a Cauchy problem for second order elliptic equations
Author(s) -
Johansson Tomas
Publication year - 2004
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310188
Subject(s) - mathematics , boundary value problem , cauchy distribution , elliptic operator , convergence (economics) , iterative method , initial value problem , cauchy's convergence test , order (exchange) , elliptic partial differential equation , operator (biology) , mathematical analysis , cauchy problem , space (punctuation) , semi elliptic operator , cauchy boundary condition , free boundary problem , partial differential equation , mathematical optimization , differential operator , computer science , repressor , economic growth , chemistry , operating system , biochemistry , transcription factor , finance , economics , gene
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 L 2 space is included. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)