Anisotropic Surface Measures as Limits of Volume Fractions View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2018

AUTHORS

Luigi Ambrosio , Giovanni E. Comi

ABSTRACT

In this paper we consider the new characterization of the perimeter of a measurable set in \(\mathbb {R}^{n}\) recently studied by Ambrosio, Bourgain, Brezis and Figalli. We modify their approach by using, instead of cubes, covering families made by translations of a given open bounded set with Lipschitz boundary. We show that the new functionals converge to an anisotropic surface measure, which is indeed a multiple of the perimeter if we allow for isotropic coverings (e.g. balls or arbitrary rotations of the given set). This result underlines that the particular geometry of the covering sets is not essential. More... »

PAGES

1-32

References to SciGraph publications

  • 1989-07. A sharp form of Poincaré type inequalities on balls and spheres in ZEITSCHRIFT FÜR ANGEWANDTE MATHEMATIK UND PHYSIK
  • Book

    TITLE

    Current Research in Nonlinear Analysis

    ISBN

    978-3-319-89799-8
    978-3-319-89800-1

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-319-89800-1_1

    DOI

    http://dx.doi.org/10.1007/978-3-319-89800-1_1

    DIMENSIONS

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