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Some Fine Properties of BV Functions on Wiener Spaces

100%

Ambrosio L., Miranda Jr. M., Pallara D.

Analysis and Geometry in Metric Spaces

2015

tom 3

nr 1

In this paper we define jump set and approximate limits for BV functions on Wiener spaces and show that the weak gradient admits a decomposition similar to the finite dimensional case. We also define the SBV class of functions of special bounded variation and give a characterisation of SBV via a chain rule and a closure theorem. We also provide a characterisation of BV functions in terms of the short-time behaviour of the Ornstein-Uhlenbeck semigroup following an approach due to Ledoux.

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On second \(\kappa\)-variation

80%

Ereú J. J., Lopez L. M., Merentes N. J.

Commentationes Mathematicae

2016

tom 56

nr 2

We present the notion of bounded second \(\kappa\)-variation for real functions defined on an interval \([a,b]\). We introduce the class \(\kappa BV^{2}([a,b])\) of all functions of bounded second \(\kappa\)-variation on \([a,b]\). We show several properties of this class and present a sufficient condition under which a composition operator acts between these spaces.

Relaxation and Integral Representation for Functionals of Linear Growth on Metric Measure spaces

70%

Hakkarainen H., Kinnunen J., Lahti P., Lehtelä P.

Analysis and Geometry in Metric Spaces

2016

tom 4

nr 1

This article studies an integral representation of functionals of linear growth on metric measure spaces with a doubling measure and a Poincaré inequality. Such a functional is defined via relaxation, and it defines a Radon measure on the space. For the singular part of the functional, we get the expected integral representation with respect to the variation measure. A new feature is that in the representation for the absolutely continuous part, a constant appears already in the weighted Euclidean case. As an application we show that in a variational minimization problem involving the functional, boundary values can be presented as a penalty term.

Ograniczanie wyników

2 Analysis and Geometry in Metric Spaces

1 Commentationes Mathematicae

1 Ambrosio L.

1 Ereú J. J.

1 Hakkarainen H.

1 Kinnunen J.

1 Lahti P.

1 Lehtelä P.

1 Lopez L. M.

1 Merentes N. J.

1 Miranda Jr. M.

1 Pallara D.

2 2016

1 2015

Wyniki wyszukiwania

Some Fine Properties of BV Functions on Wiener Spaces

On second \(\kappa\)-variation

Relaxation and Integral Representation for Functionals of Linear Growth on Metric Measure spaces