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Zbl 1195.49052
Ambrosio, Luigi
The theory of perimeters by Caccioppoli-de Giorgi and the recent developments. (La teoria dei perimetri di Caccioppoli-de Giorgi e i suoi più recenti sviluppi.)
(English)
[J] Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 21, No. 3, 275-286 (2010). ISSN 1120-6330; ISSN 1720-0768/e

Summary: We illustrate the theory of sets of finite perimeter, starting from the pioneering intuitions of Caccioppoli and De Giorgi's seminal papers. In the second part of the paper we illustrate some more recent developments and open problems in metric measure spaces, in Carnot groups and in infinite-dimensional Gaussian spaces.
MSC 2000:
*49Q15 Geometric measure and integration theory, etc.
49Q20 Variational problems in geometric measure-theoretic setting

Keywords: sets of finite perimeter; Caccioppoli sets; currents

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