On Hausdorff measure and an inequality due to Maz’ya

On Hausdorff measure and an inequality due to Maz’ya

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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Veröffentlicht in:Archiv der Mathematik 2020-05, Vol.114 (5), p.573-583
Hauptverfasser: Vogt, Hendrik, Voigt, Jürgen
Format: Artikel
Sprache:eng
Schlagworte:
Inequality
Mathematics
Mathematics and Statistics
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Zusammenfassung: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.
ISSN:0003-889X
1420-8938
DOI:10.1007/s00013-019-01425-3