The classical problem of the calculus of variations in the autonomous case: Relaxation and Lipschitzianity of solutions

Author:
Arrigo Cellina

Journal:
Trans. Amer. Math. Soc. **356** (2004), 415-426

MSC (2000):
Primary 49N60

Published electronically:
June 10, 2003

MathSciNet review:
2020039

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the problem of minimizing

Under the assumption that the Lagrangian is continuous and satisfies a growth assumption that does not imply superlinear growth, we provide a result on the relaxation of the functional and show that a solution to the minimum problem is Lipschitzian.

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Additional Information

**Arrigo Cellina**

Affiliation:
Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, Via Bicocca degli Arcimboldi 8, 20126 Milano, Italy

Email:
cellina@matapp.unimib.it

DOI:
https://doi.org/10.1090/S0002-9947-03-03347-6

Keywords:
Relaxation,
regularity of solutions

Received by editor(s):
September 4, 2001

Received by editor(s) in revised form:
March 28, 2003

Published electronically:
June 10, 2003

Article copyright:
© Copyright 2003
American Mathematical Society