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Journal Articles Nonlinear Analysis: Theory, Methods and Applications Year : 2019

REGULARITY RESULTS FOR SEGREGATED CONFIGURATIONS INVOLVING FRACTIONAL LAPLACIAN

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Giorgio Tortone
Alessandro Zilio
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Abstract

A. We study the regularity of segregated profiles arising from competition-diffusion models, where the diffusion process is of nonlocal type and is driven by the fractional Laplacian of power s ∈ (0, 1). Among others, our results apply to the regularity of the densities of an optimal partition problem involving the eigenvalues of the fractional Laplacian. More precisely, we show C 0,α * regularity of the density, where the exponent α * is explicit and is given by α * = s for s ∈ (0, 1/2] 2s − 1 for s ∈ (1/2, 1).
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Dates and versions

hal-03884870 , version 1 (05-12-2022)

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Giorgio Tortone, Alessandro Zilio. REGULARITY RESULTS FOR SEGREGATED CONFIGURATIONS INVOLVING FRACTIONAL LAPLACIAN. Nonlinear Analysis: Theory, Methods and Applications, 2019, 193, pp.111532. ⟨10.1016/j.na.2019.05.013⟩. ⟨hal-03884870⟩
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