ON A DEGENERATE PROBLEM IN THE CALCULUS OF VARIATIONS

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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https://hal.archives-ouvertes.fr/hal-01405468
Contributor : Pierre Bousquet <>
Submitted on : Monday, November 19, 2018 - 5:40:18 PM
Last modification on : Friday, September 20, 2019 - 3:06:04 PM
Long-term archiving on : Wednesday, February 20, 2019 - 3:59:17 PM

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  • HAL Id : hal-01405468, version 2

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Guy Bouchitté, Pierre Bousquet. ON A DEGENERATE PROBLEM IN THE CALCULUS OF VARIATIONS. Transactions of the American Mathematical Society, In press. ⟨hal-01405468v2⟩

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