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1. Some sharp Sobolev inequalities on $ BV({\mathbb{R}}^n) $

Author

Jin Dai and Shuang Mou

Subjects
sobolev inequalities, functions of bounded variation, optimal constants, Mathematics, QA1-939
Abstract

In this paper, some sharp Sobolev inequalities on $ BV({\mathbb{R}}^n) $, the space of functions of bounded variation on $ {\mathbb{R}}^n $, $ n\geq 2 $, are deduced through the $ L_p $ Brunn-Minkowski theory. We will prove that these inequalities can all imply the sharp Sobolev inequality on $ BV({\mathbb{R}}^n) $.

Published
2022
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