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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Existence theorems for parametric problems in the calculus of variations and approximation
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by Robert M. Goor PDF
Trans. Amer. Math. Soc. 223 (1976), 347-365 Request permission

Abstract:

In this paper, we investigate the parametric growth condition which arises in connection with existence theorems for parametric problems of the calculus of variations. In particular, we study conditions under which the length of a curve is dominated in a suitable sense by its “cost". We show that we may restrict our attention to local growth conditions on a particular set. Then we link the growth conditions to a certain approximation problem on this set. Finally, we prove that under suitable topological restrictions related to dimension theory, the local and global problems can be solved.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 223 (1976), 347-365
  • MSC: Primary 49A50
  • DOI: https://doi.org/10.1090/S0002-9947-1976-0425716-3
  • MathSciNet review: 0425716