Series expansion of weighted Finsler-Kato-Hardy inequalities
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| _version_ | 1866916542108663808 |
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| author | Tzirakis, Konstantinos |
| author_facet | Tzirakis, Konstantinos |
| contents | In this work, we consider weighted anisotropic Hardy inequalities and trace Hardy inequalities involving a general Finsler metric. We follow a unifying approach, by establishing first a sharp interpolation between them, extending the corresponding nonweighted version, being established recently by a different approach. Then, passing to bounded domains, we obtain successive sharp improvements by adding remainder terms involving sharp weights and optimal constants, resulting in an infinite series-type improvement. The results extend, into the Finsler context, the earlier known ones within the Euclidean setting. The generalization of our results to cones is also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1902_00899 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Series expansion of weighted Finsler-Kato-Hardy inequalities Tzirakis, Konstantinos Analysis of PDEs 35J20 (Primary) 26D10, 46E35 (Secondary) In this work, we consider weighted anisotropic Hardy inequalities and trace Hardy inequalities involving a general Finsler metric. We follow a unifying approach, by establishing first a sharp interpolation between them, extending the corresponding nonweighted version, being established recently by a different approach. Then, passing to bounded domains, we obtain successive sharp improvements by adding remainder terms involving sharp weights and optimal constants, resulting in an infinite series-type improvement. The results extend, into the Finsler context, the earlier known ones within the Euclidean setting. The generalization of our results to cones is also discussed. |
| title | Series expansion of weighted Finsler-Kato-Hardy inequalities |
| topic | Analysis of PDEs 35J20 (Primary) 26D10, 46E35 (Secondary) |
| url | https://arxiv.org/abs/1902.00899 |