Abstract
We present a method for proving the existence of solutions to a class of one dimensional variational problems, namely those where the Lagrangian is strongly elliptic. The method is demonstrated by some examples of optimal interpolation problems which are motivated by applications to the mechanics and control of rigid bodies. In each case the key step is to show that the variational problem satisfies the Palais–Smale condition. We do so in a general setting, showing that the number of initial conditions required depends on the higher order energy bounding properties of the Lagrangian.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
