Critical, stability and higher-order analysis for Hardy type inequalities on Cartan-Hadamard manifolds
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866918141348544512 |
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| author | Roychowdhury, Prasun Suragan, Durvudkhan Yessirkegenov, Nurgissa |
| author_facet | Roychowdhury, Prasun Suragan, Durvudkhan Yessirkegenov, Nurgissa |
| contents | In this paper, we focus on three main objectives related to Hardy-type inequalities on Cartan-Hadamard manifolds. Firstly, we explore critical Hardy-type inequalities that contain logarithmic terms, highlighting their significance. Secondly, we examine the stability of both critical and subcritical cases of the Hardy inequality. Lastly, we establish two weighted Hardy-type inequalities where singularities appear at the origin as well as boundary and we discuss their implications for higher-order operators. Our results improve upon previous findings and also present new higher-order versions of these inequalities as additional outcomes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_10655 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Critical, stability and higher-order analysis for Hardy type inequalities on Cartan-Hadamard manifolds Roychowdhury, Prasun Suragan, Durvudkhan Yessirkegenov, Nurgissa Analysis of PDEs 26D10, 35A23 In this paper, we focus on three main objectives related to Hardy-type inequalities on Cartan-Hadamard manifolds. Firstly, we explore critical Hardy-type inequalities that contain logarithmic terms, highlighting their significance. Secondly, we examine the stability of both critical and subcritical cases of the Hardy inequality. Lastly, we establish two weighted Hardy-type inequalities where singularities appear at the origin as well as boundary and we discuss their implications for higher-order operators. Our results improve upon previous findings and also present new higher-order versions of these inequalities as additional outcomes. |
| title | Critical, stability and higher-order analysis for Hardy type inequalities on Cartan-Hadamard manifolds |
| topic | Analysis of PDEs 26D10, 35A23 |
| url | https://arxiv.org/abs/2403.10655 |