On Hausdorff measure and an inequality due to Maz'ya
arXiv:1910.07837 · doi:10.1007/s00013-019-01425-3
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.