Extremizer Stability of Higher-order Hardy-Rellich inequalities for Baouendi--Grushin vector fields
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arXiv
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| Format: | Preprint |
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2025
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| author | Banerjee, Avas Basak, Riju Roychowdhury, Prasun |
| author_facet | Banerjee, Avas Basak, Riju Roychowdhury, Prasun |
| contents | In this paper, we improve the $L^p$-Rellich and Hardy-Rellich inequalities in the setting of radial Baouendi-Grushin vector fields. We establish an identity relating the subcritical and critical Hardy inequalities, thereby demonstrating their equivalence. Moreover, we obtain improved versions of these inequalities via an analysis of extremizer stability. In the higher-order setting, we derive Hardy-Rellich type inequalities involving all radial operators in the Grushin framework and prove that all resulting constants are sharp. Finally, for the $L^2$-higher-order cases, we compute exact remainder terms by establishing identities rather than inequalities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19864 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extremizer Stability of Higher-order Hardy-Rellich inequalities for Baouendi--Grushin vector fields Banerjee, Avas Basak, Riju Roychowdhury, Prasun Analysis of PDEs Classical Analysis and ODEs Functional Analysis 26D10, 35H10, 42B37 In this paper, we improve the $L^p$-Rellich and Hardy-Rellich inequalities in the setting of radial Baouendi-Grushin vector fields. We establish an identity relating the subcritical and critical Hardy inequalities, thereby demonstrating their equivalence. Moreover, we obtain improved versions of these inequalities via an analysis of extremizer stability. In the higher-order setting, we derive Hardy-Rellich type inequalities involving all radial operators in the Grushin framework and prove that all resulting constants are sharp. Finally, for the $L^2$-higher-order cases, we compute exact remainder terms by establishing identities rather than inequalities. |
| title | Extremizer Stability of Higher-order Hardy-Rellich inequalities for Baouendi--Grushin vector fields |
| topic | Analysis of PDEs Classical Analysis and ODEs Functional Analysis 26D10, 35H10, 42B37 |
| url | https://arxiv.org/abs/2504.19864 |