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EnglishAbstract We give a notion of BV function on an oriented manifold where a volume form and a family of lower semicontinuous quadratic forms Gp:TpM→[0,∞] are given. When we consider sub-Riemannian manifolds, our definition coincides with the one given in the more general context of metric measure spaces which are doubling and support a Poincaré inequality. We focus on finite perimeter sets, i.e., sets whose characteristic function is BV, in sub-Riemannian manifolds. Under an assumption on the nilpotent approximation, we prove a blowup theorem, generalizing the one obtained for step-2 Carnot groups in [24].
First we study in detail the tensorization properties of weak gradients in metric measure spaces $(X,d,mm)$. Then, we compare potentially different notions of Sobolev space $H^{1,1}(X,d,mm)$ and of weak gradient with exponent 1. Eventually we apply these results to compare the area functional $intsqrt{1+| abla f|_w^2},dmm$ with the perimeter of the subgraph of $f$, in the same spirit as the classical theory.
| Titolo: | BV functions and sets of finite perimeter in sub-Riemannian manifolds | |
| Autori: | ||
| Data di pubblicazione: | 2015 | |
| Rivista: | ||
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.anihpc.2014.01.005 | |
| Settore Scientifico Disciplinare: | Settore MAT/05 - Analisi Matematica | |
| Handle: | http://hdl.handle.net/11384/60321 | |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
File in questo prodotto:
| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| Ambrosio_Ghezzi_Magnani.pdf | Published version | Non pubblico | Open Access Visualizza/Apri | |
| Ambrosio_Magnani_Ghezzi.pdf | Post-Print | Accepted version (post-print) | Non pubblico | Administrator Richiedi una copia |
http://hdl.handle.net/11384/60321
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