Regularity of shape optimizers for some spectral fractional problems

Tortone, Giorgio

doi:10.1016/j.jfa.2021.109271

Journal of Functional Analysis

2021

DOI: 10.1016/j.jfa.2021.109271

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Regularity of shape optimizers for some spectral fractional problems

Giorgio Tortone

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Cited by 2 publications

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A vectorial problem with thin free boundary

De Silva,

Tortone

2023

Calc. Var.

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We consider the vectorial analogue of the thin free boundary problem introduced by Caffarelli et al. (J Eur math Soc 12:1151-1179, 2010) as a realization of a nonlocal version of the classical Bernoulli problem. We study optimal regularity, nondegeneracy, and density properties of local minimizers. Via a blow-up analysis based on a Weiss type monotonicity formula, we show that the free boundary is the union of a “regular” and a “singular” part. Finally we use a viscosity approach to prove $$C^{1,\alpha }$$ C 1 , α regularity of the regular part of the free boundary.

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A vectorial problem with thin free boundary

De Silva,

Tortone

2023

Calc. Var.

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Global minimizers of coexistence for strongly competing systems involving the square root of the Laplacian

He,

Zhang,

Liu

2024

Journal of Differential Equations

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Regularity of shape optimizers for some spectral fractional problems

Cited by 2 publications

References 36 publications

A vectorial problem with thin free boundary

A vectorial problem with thin free boundary

Global minimizers of coexistence for strongly competing systems involving the square root of the Laplacian

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