Publications
Published papers
N. Soave, H. Tavares and A. Zilio, "Free boundary problems with long-range interactions: uniform Lipschitz estimates in the radius", Mathematische Annalen, 386: 551–585, 2023. (pdf)
H. Tavares and A. Zilio, “Regularity of all minimizers of a class of spectral partition problems", Mathematics in Engineering, 3(1): 1-31, 2021. (pdf)
H. Berestycki and A. Zilio, “Predators-prey models with competition, Part III: classification of stationary solutions”, Dicrete and Continuous Dynamical Systems 39(12): 7141-7162, 2019. (pdf)
G. Lerario, S. V. Koniakhin, A. Maître, D. Solnyshkov, A. Zilio, Q. Glorieux, G. Malpuech, E. Giacobino, S. Pigeon, and A. Bramati, "Parallel dark-soliton pair in a bistable two-dimensional exciton-polariton superfluid", Phys. Rev. Research 2, 042041(R) , 2020. (pdf)
G. Tortone and A. Zilio, "Regularity of segregated configurations involving the fractional Laplacian", Nonlinear Analysis: Theory, Methods & Applications, 193:193, 2020. (pdf)
H. Berestycki and A. Zilio, “Predators-prey models with competition: the emergence of packs and territoriality”, The American Naturalist 193(3): 436-446, 2019.
S. Terracini, G. Verzini and A. Zilio "Spiraling asymptotic profiles of competition-diffusion systems", Communications in Pure and Applied Mathematics 72(12):2578-2620, 2019. (pdf)
L. Girardin and A. Zilio, "Competition in periodic media: III -- Existence & stability of segregated periodic coexistence states", J Dyn Diff Equat, 32:257-279, 2020. (pdf)
H. Berestycki and A. Zilio, “Predators-prey models with competition, Part I: existence, bifurcation and qualitative properties”, Communications in Contemporary Mathematics 20(07):1850010, 2018. (pdf)
N. Soave, H. Tavares, S. Terracini and A. Zilio, “Variational problems with long-range interactions”, Arch. Ration. Mech. Anal., 228(3):743-772, 2018. (pdf)
N. Soave and A. Zilio, "On phase separation in systems of coupled elliptic equations: asymptotic analysis and geometric aspects", Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire, 34(3):625-654, 2017 (pdf)
N. Soave and A. Zilio, "Multidimensional entire solutions for an elliptic system modelling phase separation", Analysis & PDE, 9(5):1019-1041, 2016 (pdf)
S. Terracini, G. Verzini, and A. Zilio. "Uniform Hölder bounds for strongly competing systems involving the square root of the laplacian", J. Eur. Math. Soc. 18(12):2865-2924, 2016. (pdf)
A. Zilio. "Optimal regularity results related to a partition problem involving the half-laplacian", New Trends in Shape Optimization, 2016. (pdf)
C.D. Pagani, D. Pierotti, G. Verzini and A. Zilio. "A nonlinear Steklov problem arising in corrosion modeling", Contributions to Nonlinear Elliptic Equations and Systems, 2015. (pdf)
N. Soave and H. Tavares, S. Terracini, A. Zilio, "Holder bounds and regularity of the emerging free boundaries for strongly competing Schrodinger equations with nontrivial grouping", Nonlinear Analysis: Theory, Methods & Applications, 2015 (pdf)
N. Soave and A. Zilio. "Uniform bounds for strongly competing systems: the optimal Lipschitz case", Arch. Ration. Mech. Anal., 218(2):647-697, 2015. (pdf)
S. Perotto and A. Zilio, "Space-time adaptive hierarchical model reduction for parabolic equations", Advanced Modeling and Simulation in Engineering Science, 2:25, 2015.
N. Soave and A. Zilio. "Entire solutions with exponential growth for an elliptic system modelling phase separation", Nonlinearity, 27(2):305-342, 2014. (pdf)
G. Verzini, and A. Zilio. "Strong competition versus fractional diffusion: the case of Lotka-Volterra interaction", Comm. Partial Differential Equations, 39(12):2284-2313, 2014. (pdf)
S. Terracini, G. Verzini, and A. Zilio. "Uniform Holder regularity with small exponent in competition-fractional diffusion systems", Discrete Contin. Dyn. Syst., 34(6):2669-2691,2014. (pdf)
S. Perotto, A. Zilio, "Hierarchical model reduction: three different approaches", Numerical Mathematics and Advanced Applications 2011, 851-859, 2014.
Link to my MathSciNet page,
Preprints
H. Berestycki and A. Zilio, “Predators-prey models with competition, Part II: uniform regularity estimates", 2019.
A. Salort, S. Terracini, G. Verzini, A. Zilio, "Rotating Spirals in segregated reaction-diffusion systems", 2022. (pdf)
My Ph.D. thesis
On monotonicity formulae, fractional operators and strong competition defense February 20, 2014
Referees: Prof. Norman Dancer, Prof. Alberto Farina, Prof. Nicola Garofalo
Jury: Prof. Alberto Farina, Prof. Fausto Gozzi, Prof. Alain Miranville