Structure of extremals for one-dimensional variational problems arising in continuum mechanics
In this paper, the structure of optimal solutions of the variational problem \[ \int^T_0 f(w(t),w'(t),w''(t))dt\to \min,\quad w\in A^T_{x,y}, \] is investigated, where \(T>0\), \((x,y)\in\mathbb{R}^2\), \[ A^T_{x,y}= \{v\in W^{2,1}([0,T]): x= (v(0),v'(0)), y=(v(T),v'(T))\}, \] \(W^{2,1}[(0,T)]\subset C^1\) is the Sobolev space of functions having second derivative and \(f\) belongs to a space of certain properties of functions. The main results of the paper are the proof of the existence of good configurations and the turnpike property of the integrand \(f\).
scientific article; zbMATH DE number 906461