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({...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2022-07-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022925?viewType=HTML |
| _version_ | 1818161034631839744 |
|---|---|
| author | Jin Dai Shuang Mou |
| author_facet | Jin Dai Shuang Mou |
| author_sort | Jin Dai |
| collection | DOAJ |
| description | 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) $. |
| first_indexed | 2024-12-11T16:11:21Z |
| format | Article |
| id | doaj.art-b6b56d50b94e4246ba08a6aee3841077 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-11T16:11:21Z |
| publishDate | 2022-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-b6b56d50b94e4246ba08a6aee38410772022-12-22T00:59:04ZengAIMS PressAIMS Mathematics2473-69882022-07-0179168511686810.3934/math.2022925Some sharp Sobolev inequalities on $ BV({\mathbb{R}}^n) $Jin Dai 0Shuang Mou1School of Mathematics and Statistics, Shaanxi Normal University, Xi'an, 710119, ChinaSchool of Mathematics and Statistics, Shaanxi Normal University, Xi'an, 710119, ChinaIn 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) $.https://www.aimspress.com/article/doi/10.3934/math.2022925?viewType=HTMLsobolev inequalitiesfunctions of bounded variationoptimal constants |
| spellingShingle | Jin Dai Shuang Mou Some sharp Sobolev inequalities on $ BV({\mathbb{R}}^n) $ AIMS Mathematics sobolev inequalities functions of bounded variation optimal constants |
| title | Some sharp Sobolev inequalities on $ BV({\mathbb{R}}^n) $ |
| title_full | Some sharp Sobolev inequalities on $ BV({\mathbb{R}}^n) $ |
| title_fullStr | Some sharp Sobolev inequalities on $ BV({\mathbb{R}}^n) $ |
| title_full_unstemmed | Some sharp Sobolev inequalities on $ BV({\mathbb{R}}^n) $ |
| title_short | Some sharp Sobolev inequalities on $ BV({\mathbb{R}}^n) $ |
| title_sort | some sharp sobolev inequalities on bv mathbb r n |
| topic | sobolev inequalities functions of bounded variation optimal constants |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022925?viewType=HTML |
| work_keys_str_mv | AT jindai somesharpsobolevinequalitiesonbvmathbbrn AT shuangmou somesharpsobolevinequalitiesonbvmathbbrn |