Journal: American Journal of Mathematics

Abbreviation

Am. j. math.

Publisher

Johns Hopkins University Press

Journal Volumes

ISSN

0002-9327
1080-6377

Description

Filters

2012 - 201932020 - 20253
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Publications 1 - 6 of 6
  • On Moments of Twisted L-Functions
    Item type: Journal Article
    Blomer, Valentin; Fouvry, Étienne; Kowalski, Emmanuel; et al. (2017)
    American Journal of Mathematics
  • Moments and Valuations
    Item type: Journal Article
    Haberl, Christoph; Parapatits, Lukas (2016)
    American Journal of Mathematics
  • Law of large numbers for the spectral radius of random matrix products
    Item type: Journal Article
    Aoun, Richard; Sert, Çagri (2021)
    American Journal of Mathematics
    We prove that the spectral radius of an i.i.d. random walk on GLd(C) satisfies a strong law of large numbers under finite second moment assumption and a weak law of large numbers under finite first moment. No irreducibility assumption is supposed. © 2021 by Johns Hopkins University Press
  • Nearly round spheres look convex
    Item type: Journal Article
    Figalli, Alessio; Rifford, Ludovic; Villani, Cédric (2012)
    American Journal of Mathematics
  • Improvement of flatness for nonlocal phase transitions
    Item type: Journal Article
    Dipierro, Serena; Serra, Joaquim; Valdinoci, Enrico (2020)
    American Journal of Mathematics
  • Stable solutions to the fractional Allen-Cahn equation in the nonlocal perimeter regime
    Item type: Journal Article
    Cabré , Xavier; Cinti , Eleonora; Serra , Joaquim (2025)
    American Journal of Mathematics
    We study stable solutions to the fractional Allen-Cahn equation (−∆)s/2u= u−u3, |u|< 1 in Rn. For every s ∈ (0, 1) and dimension n ≥ 2, we establish sharp energy estimates, density estimates, and the convergence of blow-downs to stable nonlocal s-minimal cones. As a consequence, we obtain a new classification result: if for some pair (n, s), with n ≥ 3, hyperplanes are the only stable nonlocal s-minimal cones in Rn \ {0}, then every stable solution to the fractional Allen-Cahn equation in Rn is 1D, namely, its level sets are parallel hyperplanes. Combining this result with the classification of stable s-minimal cones in R3 \ {0} for s ∼ 1 obtained by the authors in a recent paper, we give positive answers to the “stability conjecture” in R3 and to the “De Giorgi conjecture” in R4 for the fractional Allen-Cahn equation when the order s ∈ (0, 1) of the operator is sufficiently close to 1.
Publications 1 - 6 of 6