@article{Dai2022, 
author = {Jin Dai and Shuang Mou},
title = {Some sharp Sobolev inequalities on    B  V  (                    R              n    )},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {9},
pages = {16851-16868},
keywords = {Sobolev inequalities, functions of bounded variation, optimal constants},
url = {https://www.sciopen.com/article/10.3934/math.2022925},
doi = {10.3934/math.2022925},
abstract = {In this paper, some sharp Sobolev inequalities on    B  V  (                    R              n    ), the space of functions of bounded variation on                      R              n  ,    n  ≥  2, are deduced through the        L    p   Brunn-Minkowski theory. We will prove that these inequalities can all imply the sharp Sobolev inequality on    B  V  (                    R              n    ).}
}