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

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

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({...

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Bibliographic Details
Main Authors: Jin Dai, Shuang Mou
Format: Article
Language:English
Published: AIMS Press 2022-07-01
Series:AIMS Mathematics
Subjects:
sobolev inequalities
functions of bounded variation
optimal constants
Online Access:https://www.aimspress.com/article/doi/10.3934/math.2022925?viewType=HTML

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https://www.aimspress.com/article/doi/10.3934/math.2022925?viewType=HTML

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