RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Trudy Inst. Mat. i Mekh. UrO RAN: Year: Volume: Issue: Page: Find

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

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.

Full text: PDF file (248 kB)
References: PDF file   HTML file

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

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
\Bibitem{Leo12} \by A.~S.~Leonov \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 \yr 2012 \vol 18 \issue 1 \pages 198--212 \mathnet{http://mi.mathnet.ru/timm789} \elib{http://elibrary.ru/item.asp?id=17358688} \transl \jour Proc. Steklov Inst. Math. (Suppl.) \yr 2013 \vol 280 \issue , suppl. 1 \pages 119--133 \crossref{https://doi.org/10.1134/S0081543813020107} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000317236500010} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84875992150} 

• http://mi.mathnet.ru/eng/timm789
• http://mi.mathnet.ru/eng/timm/v18/i1/p198

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
•  Number of views: This page: 187 Full text: 62 References: 32 First page: 2