A note on the regularity and the existence of Riemannian splines
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866911968628047872 |
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| author | Corona, Dario Giambò, Roberto Piccione, Paolo |
| author_facet | Corona, Dario Giambò, Roberto Piccione, Paolo |
| contents | In this paper, we present a comprehensive proof concerning the regularity of critical points for the spline energy functional on Riemannian manifolds, even for the general higher-order case. Although this result is widely acknowledged in the literature, a detailed proof was previously absent. Our proof relies on a generalization of the DuBois-Reymond Lemma. Furthermore, we establish the existence of minimizers for the spline energy functional in cases where multiple interpolation points are prescribed alongside just one velocity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18408 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on the regularity and the existence of Riemannian splines Corona, Dario Giambò, Roberto Piccione, Paolo Analysis of PDEs Differential Geometry Optimization and Control 49J15 In this paper, we present a comprehensive proof concerning the regularity of critical points for the spline energy functional on Riemannian manifolds, even for the general higher-order case. Although this result is widely acknowledged in the literature, a detailed proof was previously absent. Our proof relies on a generalization of the DuBois-Reymond Lemma. Furthermore, we establish the existence of minimizers for the spline energy functional in cases where multiple interpolation points are prescribed alongside just one velocity. |
| title | A note on the regularity and the existence of Riemannian splines |
| topic | Analysis of PDEs Differential Geometry Optimization and Control 49J15 |
| url | https://arxiv.org/abs/2407.18408 |