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