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Main Authors: Corona, Dario, Giambò, Roberto, Piccione, Paolo
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2407.18408
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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