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B-Spline Solutions of General Euler-Lagrange Equations

School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China
School of Mathematical Sciences, Dalian University of Technology, Dalian 116023, China
Author to whom correspondence should be addressed.
Mathematics 2019, 7(4), 365;
Received: 28 March 2019 / Revised: 13 April 2019 / Accepted: 15 April 2019 / Published: 22 April 2019
(This article belongs to the Special Issue Discrete and Computational Geometry)
PDF [847 KB, uploaded 22 April 2019]


The Euler-Lagrange equations are useful for solving optimization problems in mechanics. In this paper, we study the B-spline solutions of the Euler-Lagrange equations associated with the general functionals. The existing conditions of B-spline solutions to general Euler-Lagrange equations are given. As part of this work, we present a general method for generating B-spline solutions of the second- and fourth-order Euler-Lagrange equations. Furthermore, we show that some existing techniques for surface design, such as Coons patches, are exactly the special cases of the generalized Partial differential equations (PDE) surfaces with appropriate choices of the constants. View Full-Text
Keywords: Lagrangian functional; Euler-Lagrange equation; B-spline surfaces; harmonic operator Lagrangian functional; Euler-Lagrange equation; B-spline surfaces; harmonic operator

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Sun, L.; Zhu, C. B-Spline Solutions of General Euler-Lagrange Equations. Mathematics 2019, 7, 365.

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