Published Paper

Inserted: 7 may 2025

Journal: Mathematics of Control, Signals, and Systems
Pages: 35
Year: 2025
Doi: https://doi.org/10.1007/s00498-025-00414-y

Abstract:

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 Lemma of DuBois-Reymond. Furthermore, we establish the existence of minimizers for the spline energy functional in cases where multiple interpolation points are prescribed alongside just one velocity.