Structure of extremals for one-dimensional variational problems arising in continuum mechanics
type: Item
instance of: scholarly article
title: Structure of extremals for one-dimensional variational problems arising in continuum mechanics
zbMATH Open document ID: 0881.49001
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-01-22T00:00:00Z
review text: 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 \(f\).
Mathematics Subject Classification ID: 49J05
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74P10
zbMATH DE Number: 906461
zbMATH Keywords: optimal solutions
zbMATH Keywords: variational problem
zbMATH Keywords: good configurations
zbMATH Keywords: turnpike property
author: Alexander J. Zaslavski
reviewed by: István Ecsedi
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0120
OpenAlex ID: W2016739948
DOI: 10.1006/JMAA.1996.0120
description: scientific article; zbMATH DE number 906461