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June  2010, 28(2): 591-606. doi: 10.3934/dcds.2010.28.591

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

Luigi Ambrosio 1, , Michele Miranda jr. 2, and  Diego Pallara 3,

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, Italy
3. 

Dipartimento di Matematica "Ennio De Giorgi”, Università del Salento, C.P. 193, Lecce, I-73100, Italy

Received  January 2010 Revised  April 2010 Published  April 2010

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.
Keywords: sets with finite perimeter, rectifiability., Wiener spaces.
Mathematics Subject Classification: Primary: 28C20, 49Q15, 26E15; Secondary: 60H0.
Citation: Luigi Ambrosio, Michele Miranda jr., Diego Pallara. Sets with finite perimeter in Wiener spaces, perimeter measure and boundary rectifiability. Discrete & Continuous Dynamical Systems, 2010, 28 (2) : 591-606. doi: 10.3934/dcds.2010.28.591
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