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Trudy Inst. Mat. i Mekh. UrO RAN, 2012, Volume 18, Number 1, Pages 198–212 (Mi timm789)  

This article is cited in 1 scientific paper (total in 1 paper)

Higher-order total variations for functions of several variables and their application in the theory of ill-posed problems

A. S. Leonov

National Engineering Physics Institute "MEPhI"

Abstract: In the space of functions of two variables with Hardy–Krause property, new notions of higher-order total variations and Banach spaces of functions of two variables with bounded higher variations are introduced. The connection of these spaces with Sobolev spaces $W^m_1$, $m\in\mathbb N$, is studied. In Sobolev spaces, a wide class of integral functionals with the weak regularization properties and the $H$-property is isolated. It is proved that the application of these functionals in the Tikhonov variational scheme generates for $m\ge3$ the convergence of approximate solutions with respect to the total variation of order $m-3$. The results are naturally extended to the case of functions of $N$ variables.

Keywords: higher-order total variations for functions of several variables, regularization of ill-posed problems.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2013, 280, suppl. 1, 119–133

Bibliographic databases:

Document Type: Article
UDC: 517.397
Received: 26.04.2011

Citation: A. S. Leonov, “Higher-order total variations for functions of several variables and their application in the theory of ill-posed problems”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 1, 2012, 198–212; Proc. Steklov Inst. Math. (Suppl.), 280, suppl. 1 (2013), 119–133

Citation in format AMSBIB
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\paper Higher-order total variations for functions of several variables and their application in the theory of ill-posed problems
\serial Trudy Inst. Mat. i Mekh. UrO RAN
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\vol 18
\issue 1
\pages 198--212
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2013
\vol 280
\issue , suppl. 1
\pages 119--133
\crossref{https://doi.org/10.1134/S0081543813020107}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. V. Vasin, “Regularization of Ill-Posed Problems By Using Stabilizers in the Form of the Total Variation of a Function and Its Derivatives”, J. Inverse Ill-Posed Probl., 24:2 (2016), 149–158  crossref  mathscinet  zmath  isi  elib  scopus
  • Trudy Instituta Matematiki i Mekhaniki UrO RAN
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