On nonexistence of minimizing solutions of variational problems
type: Item
instance of: scholarly article
title: On nonexistence of minimizing solutions of variational problems
zbMATH Open document ID: 0592.49030
DOI: 10.1016/0022-247X(86)90072-7
author: Fopke Klok
published in: Journal of Mathematical Analysis and Applications
publication date: 1986-01-01T00:00:00Z
review text: Considered is the minimum problem for a functional of the type \(\int^{T}_{0}L(\gamma (t),{\dot \gamma}(t))dt.\) Here, L is supposed to be a smooth function of its arguments. For the admissible curves \(\gamma\) : [0,T]\(\to {\mathbb{R}}^ n\) the endpoints \(\gamma (0)=x_ 0\) and \(\gamma (T)=x_ 1\) are prescribed. The author is interested in problems without solution where the Lagrangian L does not necessarily satisfy a convexity assumption so that the associated Hamiltonian vector field is no longer continuous everywhere. A class of such problems is studied for arbitrary dimension n. It is shown that the nonexistence of solutions is caused by the presence of some local type of discontinuity in the Hamiltonian vector field.
Mathematics Subject Classification ID: 49Q20
Mathematics Subject Classification ID: 49J45
zbMATH DE Number: 3951419
zbMATH Keywords: minimum problem
reviewed by: Waldemar Velte
MaRDI profile type: Publication
cites work: Q4174811
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description: scientific article; zbMATH DE number 3951419