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On Hausdorff measure and an inequality due to Maz’ya

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Abstract

We give an “elementary” proof of an inequality due to Maz’ya. As a prerequisite we prove an approximation property for the Hausdorff measure. We also comment on the relations between Maz’ya’s inequality, the isoperimetric inequality, and the Sobolev inequality.

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Authors and Affiliations

  1. Fachbereich Mathematik, Universität Bremen, Postfach 330 440, 28359, Bremen, Germany

    Hendrik Vogt

  2. Fakultät Mathematik, Technische Universität Dresden, 01062, Dresden, Germany

    Jürgen Voigt

Authors
  1. Hendrik Vogt
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  2. Jürgen Voigt
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Correspondence to Jürgen Voigt.

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Vogt, H., Voigt, J. On Hausdorff measure and an inequality due to Maz’ya. Arch. Math. 114, 573–583 (2020). https://doi.org/10.1007/s00013-019-01425-3

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  • DOI: https://doi.org/10.1007/s00013-019-01425-3

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