@article{d477ab0d92ef4f579917c6fa03a0911f,

title = "AN ELASTIC FLOW FOR NONLINEAR SPLINE INTERPOLATIONS IN ℝn",

abstract = "In this paper we use the method of geometric flow on the problem of nonlinear spline interpolations for non-closed curves in n-dimensional Euclidean spaces. The method applies theory of fourth-order parabolic PDEs to each piece of the curve between two successive knot points at which certain dynamic boundary conditions are imposed. We show the existence of global solutions of the elastic flow in suitable H{\"o}lder spaces. In the asymptotic limit, as time approaches infinity, solutions subconverge to a stationary solution of the problem. The method of geometric flows provides a new approach for the problem of nonlinear spline interpolations.",

keywords = "Fourth-order geometric flow, curve fitting, elastic spline, spline interpolation",

author = "Lin, {Chun Chi} and Schwetlick, {Hartmut R.} and Tran, {Dung The}",

note = "Funding Information: Received by the editors September 9, 2012, and, in revised form, December 18, 2021. 2020 Mathematics Subject Classification. Primary 35K55; Secondary 41A15. Key words and phrases. Fourth-order geometric flow, elastic spline, spline interpolation, curve fitting. This work was partially supported by the research grant of the National Science Council of Taiwan (NSC-100-2115-M-003-003), the National Center for Theoretical Sciences at Taipei, and the Max-Planck-Institut f{\"u}r Mathematik in den Naturwissenschaften in Leipzig. The third author received financial support from Taiwan MoST 108-2115-M-003-003-MY2. Publisher Copyright: {\textcopyright} 2022 American Mathematical Society",

year = "2022",

month = jul,

day = "1",

doi = "10.1090/tran/8639",

language = "English",

volume = "375",

pages = "4893--4942",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

publisher = "American Mathematical Society",

number = "7",

}