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"
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.
higher-order total variations for functions of several variables, regularization of ill-posed problems.
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Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2013, 280, suppl. 1, 119–133
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
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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
\jour Proc. Steklov Inst. Math. (Suppl.)
\issue , suppl. 1
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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
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