ESAIM: Control, Optimisation and Calculus of Variations

Table of Contents - October 2009 - Volume 15, Issue 04  

Research Article

Structure of approximate solutions of variational problems with extended-valued convex integrands

Zaslavski, Alexander J.

Department of Mathematics, The Technion-Israel Institute of Technology, 32000 Haifa, Israel. ajzasl@tx.technion.ac.il

Abstract

In this work we study the structure of approximate solutions of autonomous variational problems with a lower semicontinuous strictly convex integrand f : Rn ×Rn $\to$ R 1 $\cup$ $\{\infty\}$ , where Rn is the n-dimensional Euclidean space. We obtain a full description of the structure of the approximate solutions which is independent of the length of the interval, for all sufficiently large intervals.

(Received June 6 2007)

(Revised May 1 2008)

(Online publication August 20 2008)

Key Words:

  • Good function;
  • infinite horizon;
  • integrand;
  • overtaking optimal function;
  • turnpike property

Mathematics Subject Classification:

  • 49J99