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Transactions of the American Mathematical Society

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

 

 

An indirect method in the calculus of variations


Author: F. H. Clarke
Journal: Trans. Amer. Math. Soc. 336 (1993), 655-673
MSC: Primary 49J05; Secondary 49J52, 49N60
DOI: https://doi.org/10.1090/S0002-9947-1993-1118823-3
MathSciNet review: 1118823
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Abstract: This article presents a new approach to the issue of the existence of solutions to the basic problem in the calculus of variations. The method is indirect, and applies to certain classes of of problems with slow or no growth, in addition to those satisfying the traditional coercivity condition. The proof hinges upon showing with the help of nonsmooth analysis that a certain value function is constant. Examples are given to illustrate the applicability of the results and the necessity of the hypotheses.


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DOI: https://doi.org/10.1090/S0002-9947-1993-1118823-3
Keywords: Existence theory, nonsmooth analysis
Article copyright: © Copyright 1993 American Mathematical Society