\(BV\) functions on open domains: the Wiener case and a Fomin differentiable case. (English) Zbl 1441.49036
Functions of bounded variation (BV functions) have had an important role in several classical problems of the calculus of variations, geometric measure theory and mathematical physics. Several authors applied BV functions to study Fourier series in several variables (see, [L. Ambrosio et al., Functions of bounded variation and free discontinuity problems. Oxford: Clarendon Press (2000; Zbl 0957.49001)], [G. Da Prato and A. Lunardi, J. Funct. Anal. 259, No. 10, 2642–2672 (2010; Zbl 1204.35172); J. Math. Pures Appl. (9) 99, No. 6, 741–765 (2013; Zbl 1293.35359)], [E. De Giorgi, Atti Accad. Naz. Lincei, VIII. Ser., Rend., Cl. Sci. Fis. Mat. Nat. 14, 390–393 (1953; Zbl 0051.29403); Ann. Mat. Pura Appl. (4) 36, 191–213 (1954; Zbl 0055.28504)], [M. Hino, J. Funct. Anal. 258, No. 5, 1656–1681 (2010; Zbl 1196.46029)], [M. Fukushima and M. Hino, J. Funct. Anal. 183, No. 1, 245–268 (2001; Zbl 0993.60049)]).
The principal objective in this paper is to provide three different characterizations of the space BV of the functions of bounded variation with respect to a centred non-degenerate Gaussian measure on open domains in Wiener spaces. Also, the authors apply techniques to Fomin differentiable probability measures on a Hilbert space.
The principal objective in this paper is to provide three different characterizations of the space BV of the functions of bounded variation with respect to a centred non-degenerate Gaussian measure on open domains in Wiener spaces. Also, the authors apply techniques to Fomin differentiable probability measures on a Hilbert space.
Reviewer: Lakehal Belarbi (Mostaganem)
MSC:
| 49Q20 | Variational problems in a geometric measure-theoretic setting |
| 58E99 | Variational problems in infinite-dimensional spaces |
| 28C20 | Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) |
| 26B30 | Absolutely continuous real functions of several variables, functions of bounded variation |
| 60H07 | Stochastic calculus of variations and the Malliavin calculus |
| 49Q15 | Geometric measure and integration theory, integral and normal currents in optimization |
Keywords:
infinite-dimensional analysis; functions of bounded variation; open domains in Wiener spaces; geometric measure theory; Fomin differentiable measuresCitations:
Zbl 0957.49001; Zbl 1204.35172; Zbl 1293.35359; Zbl 0051.29403; Zbl 0055.28504; Zbl 1196.46029; Zbl 0993.60049References:
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