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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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Regularization of ill-posed problems in Sobolev space W 1 1

A. S. Leonov

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Citation Information: Journal of Inverse and Ill-posed Problems jiip. Volume 13, Issue 6, Pages 595–619, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: 10.1515/156939405775199505,

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The problem of regularization of ill-posed problems in the Sobolev space W 1 1 is considered in the paper. Classes of regularizing functionals are described which provide strong convergence in this space when a variational approach is used for solving the ill-posed problems. This convergence in turn implies the convergence of approximate solutions in variation of functions of several variables.

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[1]
A. I. Korotkii and D. O. Mikhailova
Proceedings of the Steklov Institute of Mathematics, 2013, Volume 280, Number S1, Page 98
[2]
M.A. Korotkii
Journal of Applied Mathematics and Mechanics, 2009, Volume 73, Number 1, Page 26
[3]
Kazufumi Ito, Bangti Jin, and Jun Zou
Applicable Analysis, 2011, Volume 90, Number 10, Page 1521
[4]
Christiane Pöschl, Elena Resmerita, and Otmar Scherzer
Inverse Problems, 2010, Volume 26, Number 10, Page 105017
[5]
A. S. Leonov
Computational Mathematics and Mathematical Physics, 2007, Volume 47, Number 5, Page 732
[6]
V. V. Vasin
Journal of Inverse and Ill-posed Problems, 2006, Volume 14, Number 8, Page 813

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