REGULARITY RESULTS FOR SEGREGATED CONFIGURATIONS INVOLVING FRACTIONAL LAPLACIAN

Giorgio Tortone , Alessandro Zilio (1)

1 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions

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).

Domaines: Equations aux dérivées partielles [math.AP]

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⟩