A remark on the anisotropic outer Minkowski content

Antonin Chambolle; Stefano Lisini; Luca Lussardi

doi:10.1515/acv-2013-0103

Published by De Gruyter May 4, 2013

A remark on the anisotropic outer Minkowski content

Antonin Chambolle , Stefano Lisini and Luca Lussardi

From the journal Advances in Calculus of Variations

https://doi.org/10.1515/acv-2013-0103

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Abstract.

We study an anisotropic version of the outer Minkowski content of a closed set in ℝn. In particular, we show that it exists on the same class of sets for which the classical outer Minkowski content coincides with the Hausdorff measure, and we give its explicit form.

Keywords: Outer Minkowski content; finite perimeter sets; Γ-convergence; anisotropic perimeter

MSC: 28A75; 49Q15; 52A39

We are grateful to the referees for their encouraging remarks.

Received: 2012-3-27

Revised: 2012-12-10

Accepted: 2013-4-5

Published Online: 2013-5-4

Published in Print: 2014-4-1

A remark on the anisotropic outer Minkowski content

Abstract.

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