Sets with finite perimeter in Wiener spaces, perimeter measure and boundary rectifiability

Luigi Ambrosio; Michele Miranda jr.; Diego Pallara

doi:10.3934/dcds.2010.28.591

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2010, Volume 28, Issue 2: 591-606. Doi: 10.3934/dcds.2010.28.591 open access

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Sets with finite perimeter in Wiener spaces, perimeter measure and boundary rectifiability

1.
Scuola Normale Superiore, p.za dei Cavalieri 7, Pisa, I-56126
2.
Dipartimento di Matematica, Università di Ferrara, via Machiavelli 35, Ferrara, I-44121
3.
Dipartimento di Matematica "Ennio De Giorgi”, Università del Salento, C.P. 193, Lecce, I-73100

Received: December 31, 2009

Revised: March 31, 2010

Published: June 2010

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Abstract

We discuss some recent developments of the theory of $BV$ functionsand sets of finite perimeter in infinite-dimensional Gaussianspaces. In this context the concepts of Hausdorff measure,approximate continuity, rectifiability have to be properlyunderstood. After recalling the known facts, we prove aSobolev-rectifiability result and we list some open problems.

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Mathematics Subject Classification: Primary: 28C20, 49Q15, 26E15; Secondary: 60H07.

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