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Transactions of the American Mathematical Society

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

 
 

 

On a degenerate problem in the calculus of variations


Authors: Guy Bouchitté and Pierre Bousquet
Journal: Trans. Amer. Math. Soc. 371 (2019), 777-807
MSC (2010): Primary 35A02, 49N60, 49J45
DOI: https://doi.org/10.1090/tran/7570
Published electronically: October 17, 2018
MathSciNet review: 3885161
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Abstract: We establish the uniqueness of the solutions for a degenerate scalar problem in the multiple integrals calculus of variations. The proof requires as a preliminary step the study of the regularity properties of the solutions and of their level sets. We exploit the uniqueness and the regularity results to explore some of their qualitative properties. In particular, we emphasize the link between the supports of the solutions and the Cheeger problem.


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Additional Information

Guy Bouchitté
Affiliation: IMATH, EA 2134, Université du Sud Toulon-Var, BP 20132 - 83957 La Garde Cedex, France
Email: bouchitte@univ-tln.fr

Pierre Bousquet
Affiliation: Institut de Mathématiques de Toulouse, CNRS UMR 5219, Université de Toulouse, F-31062 Toulouse Cedex 9, France
Email: pierre.bousquet@math.univ-toulouse.fr

DOI: https://doi.org/10.1090/tran/7570
Keywords: Degenerate and singular problems, regularity and uniqueness of minimizers
Received by editor(s): November 30, 2016
Published electronically: October 17, 2018
Additional Notes: Part of this work was written during a visit of the second author to Toulon. The support of IMATH is kindly acknowledged.
Article copyright: © Copyright 2018 American Mathematical Society