On a degenerate problem in the calculus of variations

Bouchitté, Guy; Bousquet, Pierre

doi:10.1090/tran/7570

On a degenerate problem in the calculus of variations
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by Guy Bouchitté and Pierre Bousquet PDF

Trans. Amer. Math. Soc. 371 (2019), 777-807 Request permission

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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