Sharp subcritical and critical L p $L^{p}$ Hardy inequalities on the sphere
Abstract We obtain sharp inequalities of Hardy type for functions in the Sobolev space W 1 , p $W^{1,p}$ on the unit sphere S n − 1 $\mathbb{S}^{n-1}$ in R n $\mathbb{R}^{n}$ . We achieve this in both the subcritical and critical cases. The method we use to show optimality takes into account all the...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-07-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-022-02833-w |
| _version_ | 1797863223193501696 |
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| author | Ahmed A. Abdelhakim |
| author_facet | Ahmed A. Abdelhakim |
| author_sort | Ahmed A. Abdelhakim |
| collection | DOAJ |
| description | Abstract We obtain sharp inequalities of Hardy type for functions in the Sobolev space W 1 , p $W^{1,p}$ on the unit sphere S n − 1 $\mathbb{S}^{n-1}$ in R n $\mathbb{R}^{n}$ . We achieve this in both the subcritical and critical cases. The method we use to show optimality takes into account all the constants involved in our inequalities. We apply our results to obtain lower bounds for the the first eigenvalue of the p-Laplacian on the sphere. |
| first_indexed | 2024-04-09T22:33:15Z |
| format | Article |
| id | doaj.art-c9f3acb9807e4d97add4d3c3d4219eda |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-04-09T22:33:15Z |
| publishDate | 2022-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-c9f3acb9807e4d97add4d3c3d4219eda2023-03-22T12:40:23ZengSpringerOpenJournal of Inequalities and Applications1029-242X2022-07-012022112410.1186/s13660-022-02833-wSharp subcritical and critical L p $L^{p}$ Hardy inequalities on the sphereAhmed A. Abdelhakim0Department of Mathematics, College of Science and Arts in Unaizah, Qassim UniversityAbstract We obtain sharp inequalities of Hardy type for functions in the Sobolev space W 1 , p $W^{1,p}$ on the unit sphere S n − 1 $\mathbb{S}^{n-1}$ in R n $\mathbb{R}^{n}$ . We achieve this in both the subcritical and critical cases. The method we use to show optimality takes into account all the constants involved in our inequalities. We apply our results to obtain lower bounds for the the first eigenvalue of the p-Laplacian on the sphere.https://doi.org/10.1186/s13660-022-02833-wSobolev Space on manifoldsL p $L^{p}$ Hardy inequalitiesDensity agrumentUnit sphere |
| spellingShingle | Ahmed A. Abdelhakim Sharp subcritical and critical L p $L^{p}$ Hardy inequalities on the sphere Journal of Inequalities and Applications Sobolev Space on manifolds L p $L^{p}$ Hardy inequalities Density agrument Unit sphere |
| title | Sharp subcritical and critical L p $L^{p}$ Hardy inequalities on the sphere |
| title_full | Sharp subcritical and critical L p $L^{p}$ Hardy inequalities on the sphere |
| title_fullStr | Sharp subcritical and critical L p $L^{p}$ Hardy inequalities on the sphere |
| title_full_unstemmed | Sharp subcritical and critical L p $L^{p}$ Hardy inequalities on the sphere |
| title_short | Sharp subcritical and critical L p $L^{p}$ Hardy inequalities on the sphere |
| title_sort | sharp subcritical and critical l p l p hardy inequalities on the sphere |
| topic | Sobolev Space on manifolds L p $L^{p}$ Hardy inequalities Density agrument Unit sphere |
| url | https://doi.org/10.1186/s13660-022-02833-w |
| work_keys_str_mv | AT ahmedaabdelhakim sharpsubcriticalandcriticallplphardyinequalitiesonthesphere |