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

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 $BV$ functions and sets of finite perimeter in infinite-dimensional Gaussian spaces. In this context the concepts of Hausdorff measure, approximate continuity, rectifiability have to be properly understood. After recalling the known facts, we prove a Sobolev-rectifiability result and we list some open problems.
Citation: Luigi Ambrosio, Michele Miranda jr., Diego Pallara. Sets with finite perimeter in Wiener spaces, perimeter measure and boundary rectifiability. Discrete & Continuous Dynamical Systems - A, 2010, 28 (2) : 591-606. doi: 10.3934/dcds.2010.28.591
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