naa a22 4500 510811779 CHVBK 20180411083445.0 cr unu---uuuuu 180411e20130401xx s 000 0 eng 10.1134/S0081543813020107 doi (NATIONALLICENCE)springer-10.1134/S0081543813020107 Leonov A. National Research Nuclear University MEPhI, Kahisrskoe sh. 31, 115409, Moscow, Russia aut Higher-order total variations for functions of several variables and their application in the theory of ill-posed problems [Elektronische Daten] [A. Leonov] 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 the Sobolev spaces W 1 m , m ∈ ℕ, is studied. In the Sobolev spaces, a wide class of integral functionals with the weak regularization properties and the H-property is defined. It is proved that the application of these functionals in the Tikhonov variational scheme generates for m ≥ 3 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. Pleiades Publishing, Ltd., 2013 higher-order total variations for functions of several variables nationallicence regularization of ill-posed problems nationallicence Proceedings of the Steklov Institute of Mathematics SP MAIK Nauka/Interperiodica 280(2013-04-01), 119-133 0081-5438 280<119 2013 280 11501 https://doi.org/10.1134/S0081543813020107 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1134/S0081543813020107 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Leonov A. National Research Nuclear University MEPhI, Kahisrskoe sh. 31, 115409, Moscow, Russia aut NATIONALLICENCE 773 0- Proceedings of the Steklov Institute of Mathematics SP MAIK Nauka/Interperiodica 280(2013-04-01), 119-133 0081-5438 280<119 2013 280 11501 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer