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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description	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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subjects	Inequality Mathematics Mathematics and Statistics
title	On Hausdorff measure and an inequality due to Maz’ya
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