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A decomposition theorem for $BV$ functions
1. | SISSA, via Bonomea, 265, Trieste, 34136, Italy, Italy |
In this paper we generalize this property to real valued $BV$ functions of many variables, extending naturally the concept of monotone function. Our result is an extension of a result obtained by Alberti, Bianchini and Crippa.
A counterexample is given which prevents further extensions.
References:
[1] |
G. Alberti, S. Bianchini and G. Crippa, Invariants for weakly regular ODE flows,, to appear., ().
|
[2] |
L. Ambrosio, V. Caselles, S. Masnou and J. M. Morel, Connected components of sets of finite perimeter and applications to image processing, J. Eur. Math. Soc. (JEMS), 3 (2001), 39-92.
doi: 10.1007/PL00011302. |
[3] |
L. Ambrosio, N. Fusco and D. Pallara, "Functions of Bounded Variation and Free Discontinuity Problems," Oxford University Press, 2000. |
[4] | |
[5] |
P. Hajlasz and J. Malý, Approximation in Soblev spaces of nonlinear expressions involving the gradient, Ark. Mat., 40 (2002), 245-274.
doi: 10.1007/BF02384536. |
[6] |
J. J. Manfredi, Weakly monotone functions, J. Geom. Anal., 4 (1994), 393-402. |
show all references
References:
[1] |
G. Alberti, S. Bianchini and G. Crippa, Invariants for weakly regular ODE flows,, to appear., ().
|
[2] |
L. Ambrosio, V. Caselles, S. Masnou and J. M. Morel, Connected components of sets of finite perimeter and applications to image processing, J. Eur. Math. Soc. (JEMS), 3 (2001), 39-92.
doi: 10.1007/PL00011302. |
[3] |
L. Ambrosio, N. Fusco and D. Pallara, "Functions of Bounded Variation and Free Discontinuity Problems," Oxford University Press, 2000. |
[4] | |
[5] |
P. Hajlasz and J. Malý, Approximation in Soblev spaces of nonlinear expressions involving the gradient, Ark. Mat., 40 (2002), 245-274.
doi: 10.1007/BF02384536. |
[6] |
J. J. Manfredi, Weakly monotone functions, J. Geom. Anal., 4 (1994), 393-402. |
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