On a degenerate problem in the calculus of variations

On a degenerate problem in the calculus of variations

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 result...

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Veröffentlicht in:Transactions of the American Mathematical Society 2019-02, Vol.371 (2), p.777-807
Hauptverfasser: Bouchitté, Guy, Bousquet, Pierre
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Analysis of PDEs
Mathematics
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Bousquet, Pierre
description 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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title On a degenerate problem in the calculus of variations
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