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 the Sobolev spaces W 1 , 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.
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