On a general coarea inequality and applications.
Magnani, Valentino (2002)
Annales Academiae Scientiarum Fennicae. Mathematica
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Magnani, Valentino (2002)
Annales Academiae Scientiarum Fennicae. Mathematica
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Bruno Franchi, Raul Serapioni, Francesco Serra Cassano (2002)
Mathematica Bohemica
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We study finite perimeter sets in step 2 Carnot groups. In this way we extend the classical De Giorgi’s theory, developed in Euclidean spaces by De Giorgi, as well as its generalization, considered by the authors, in Heisenberg groups. A structure theorem for sets of finite perimeter and consequently a divergence theorem are obtained. Full proofs of these results, comments and an exhaustive bibliography can be found in our preprint (2001).
Franchi, Bruno, Serapioni, Raul, Cassano, Francesco Serra
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Monti, Roberto (2003)
Annales Academiae Scientiarum Fennicae. Mathematica
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Valentino Magnani (2011)
Colloquium Mathematicae
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We present an area formula for continuous mappings between metric spaces, under minimal regularity assumptions. In particular, we do not require any notion of differentiability. This is a consequence of a measure-theoretic notion of Jacobian, defined as the density of a suitable "pull-back measure". Finally, we give some applications and examples.
Bruno Franchi, Piotr Hajłasz, Pekka Koskela (1999)
Annales de l'institut Fourier
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There have been recent attempts to develop the theory of Sobolev spaces on metric spaces that do not admit any differentiable structure. We prove that certain definitions are equivalent. We also define the spaces in the limiting case .