Full list of publications


    Submitted papers

  1. P. Colli, T. Fukao, L. Scarpa.
    The Cahn-Hilliard equation with forward-backward dynamic boundary condition via vanishing viscosity.
    arXiv:2106.01010 [math.AP]

  2. L. Scarpa. and U. Stefanelli.
    Doubly nonlinear stochastic evolution equations II.
    arXiv:2009.08209 [math.AP]

    3. Accepted and published papers

  3. L. Scarpa, U. Stefanelli.
    The Energy-Dissipation Principle for stochastic parabolic equations.
    Adv. Math. Sci. Appl. (to appear).
    arXiv:2109.05882 [math.AP]

  4. E. Rocca, L. Scarpa, A. Signori.
    Parameter identification for nonlocal phase field models for tumor growth via optimal control and asymptotic analysis.
    Math. Models Methods Appl. Sci. (to appear).
    arXiv:2009.11159 [math.AP]

  5. C. Marinelli and L. Scarpa.
    Well-posedness of monotone semilinear SPDEs with semimartingale noise.
    Séminarie de Probabilités (to appear).
    arXiv:1805.07562 [math.PR]

  6. A. Menovschikov, A. Molchanova, L. Scarpa.
    An extended variational theory for nonlinear evolution equations via modular spaces.
    SIAM J. Math. Anal. 53 (2021), no. 4, 4865-4907.
    doi:10.1137/20M1385251     arXiv:2012.05518 [math.AP]

  7. L. Scarpa.
    The stochastic viscous Cahn-Hilliard equation: well-posedness, regularity and vanishing viscosity limit.
    Appl. Math. Optim. 84 (2021), no. 1, 487-533.
    doi:10.1007/s00245-020-09652-9     arXiv:1809.04871 [math.AP]

  8. L. Scarpa.
    The stochastic Cahn-Hilliard equation with degenerate mobility and logarithmic potential.
    Nonlinearity 34 (2021), no. 6, 3813-3857.
    doi:10.1088/1361-6544/abf338     arXiv:1909.12106 [math.AP]

  9. L. Scarpa and A. Signori.
    On a class of non-local phase-field models for tumor growth with possibly singular potentials, chemotaxis, and active transport.
    Nonlinearity 34 (2021), no. 5, 3199-3250.
    doi:10.1088/1361-6544/abe75d      arXiv:2002.12702 [math.AP]

  10. E. Davoli, L. Scarpa, L. Trussardi.
    Local asymptotics for nonlocal convective Cahn-Hilliard equations with W^{1,1} kernel and singular potential.
    J. Differential Equations 289 (2021), 35-58.
    doi:10.1016/j.jde.2021.04.016      arXiv:1911.12770 [math.AP]

  11. L. Scarpa.
    Analysis and optimal velocity control of a stochastic convective Cahn-Hilliard equation.
    J. Nonlinear Sci. 31 (2021), no. 2, 45.
    doi:10.1007/s00332-021-09702-8      arXiv:2007.14735 [math.AP]

  12. C. Marinelli, L. Scarpa, U. Stefanelli.
    An alternative proof of well-posedness of stochastic evolution equations in the variational setting.
    Rev. Roumaine Math. Pures Appl. 66 (2021), no. 1, 209-221.
    arXiv:2009.09700 [math.AP]

  13. E. Davoli, L. Scarpa, L. Trussardi.
    Nonlocal-to-local convergence of Cahn-Hilliard equations: Neumann boundary conditions and viscosity terms.
    Arch. Ration. Mech. Anal. 239 (2021), no. 1, 117-149.
    doi:10.1007/s00205-020-01573-9     arXiv:1908.00945 [math.AP]

  14. L. Scarpa and U. Stefanelli.
    Stochastic PDEs via convex minimization.
    Comm. Partial Differential Equations 46 (2021), no. 1, 66-97.
    doi:10.1080/03605302.2020.1831017     arXiv:2004.00337 [math.OC]

  15. C. Orrieri, E. Rocca, L. Scarpa.
    Optimal control of stochastic phase-field models related to tumor growth.
    ESAIM Control Optim. Calc. Var. 26 (2020), Paper No. 104, 46 pp.
    doi:10.1051/cocv/2020022     arXiv:1908.00306 [math.AP]

  16. L. Scarpa, U. Stefanelli.
    An order approach to SPDEs with antimonotone terms.
    Stoch. Partial Differ. Equ. Anal. Comput. 8 (2020), no. 4, 819-832.
    doi:10.1007/s40072-019-00161-7     arXiv:1910.01816 [math.AP]

  17. C. Marinelli and L. Scarpa.
    Refined existence and regularity results for a class of semilinear dissipative SPDEs.
    Infin. Dimens. Anal. Quantum Probab. Relat. Top. 23 (2020), no. 2, 2050014.
    doi:10.1142/S0219025720500149     arXiv:1711.11091 [math.AP]

  18. C. Marinelli and L. Scarpa.
    Fréchet differentiability of mild solutions to SPDEs with respect to the initial datum.
    J. Evol. Equ. 20 (2020), no. 3, 1093-1130.
    doi:10.1007/s00028-019-00546-0     arXiv:1812.09949 [math.PR]

  19. L. Scarpa and U. Stefanelli.
    Doubly nonlinear stochastic evolution equations.
    Math. Models Methods Appl. Sci. 30 (2020), no. 5, 991-1031.
    doi:10.1142/S0218202520500219     arXiv:1905.11294 [math.AP]

  20. E. Davoli, H. Ranetbauer, L. Scarpa and L. Trussardi.
    Degenerate nonlocal Cahn-Hilliard equations: well-posedness, regularity and local asymptotics.
    Ann. Inst. H. Poincaré Anal. Non Linéaire 37 (2020), no. 3, 627-651.
    doi:10.1016/j.anihpc.2019.10.002     arXiv:1902.04469 [math.AP]

  21. E. Bonetti, P. Colli, L. Scarpa, G. Tomassetti.
    Bounded solutions and their asymptotics for a doubly nonlinear Cahn-Hilliard system.
    Calc. Var. Partial Differential Equations 59 (2020), no. 2, Paper no. 88.
    doi:10.1007/s00526-020-1715-9      arXiv:1908.02079 [math.AP]

  22. C. Marinelli and L. Scarpa.
    Ergodicity and Kolmogorov equations for dissipative SPDEs with singular drift: a variational approach.
    Potential Anal. 52 (2020), no. 1, 69-103.
    doi:10.1007/s11118-018-9731-5     arXiv:1710.05612 [math.AP]

  23. L. Scarpa.
    Optimal distributed control of a stochastic Cahn-Hilliard equation.
    SIAM J. Control Optim. 57 (2019), no. 5, 3571-3602.
    doi:10.1137/18M1222223     arXiv:1810.09292 [math.OC]

  24. S. Melchionna, H. Ranetbauer, L. Scarpa and L. Trussardi.
    From nonlocal to local Cahn-Hilliard equation.
    Adv. Math. Sci. Appl. 28 (2019), no. 1, 197-211.
    arXiv:1803.09729 [math.AP]

  25. C. Orrieri and L. Scarpa.
    Singular stochastic Allen-Cahn equations with dynamic boundary conditions.
    J. Differential Equations 266 (2019), no. 8, 4624-4667.
    doi:10.1016/j.jde.2018.10.007     arXiv:1703.04099 [math.AP]

  26. L. Scarpa.
    Existence and uniqueness of solutions to singular Cahn-Hilliard equations with nonlinear viscosity terms and dynamic boundary conditions.
    J. Math. Anal. Appl. 469 (2019), no. 2, 730-764.
    doi:10.1016/j.jmaa.2018.09.034     arXiv:1802.02877 [math.AP]

  27. C. Marinelli and L. Scarpa.
    A note on doubly nonlinear SPDEs with singular drift in divergence form.
    Accad. Naz. Lincei Rend. Lincei Mat. Appl. 29 (2018), no. 4, 619-633.
    doi:10.4171/RLM/825     arXiv:1712.05595 [math.AP]

  28. C. Marinelli and L. Scarpa.
    Strong solutions to SPDEs with monotone drift in divergence form.
    Stoch. Partial Differ. Equ. Anal. Comput. 6 (2018), no. 3, 364-396.
    doi:10.1007/s40072-018-0111-3     arXiv:1612.08260 [math.AP]

  29. E. Bonetti, P. Colli, L. Scarpa. and G. Tomassetti.
    A doubly nonlinear Cahn-Hilliard system with nonlinear viscosity.
    Commun. Pure Appl. Anal. 17 (2018), no. 3, 1001-1022.
    doi:10.3934/cpaa.2018049     arXiv:1710.06698 [math.AP]

  30. C. Marinelli and L. Scarpa.
    A variational approach to dissipative SPDEs with singular drift.
    Ann. Probab. 46 (2018), no. 3, 1455-1497.
    doi:10.1214/17-AOP1207     arXiv:1604.08808 [math.AP]

  31. L. Scarpa.
    On the stochastic Cahn-Hilliard equation with a singular double-well potential.
    Nonlinear Anal. 171 (2018), 102-133.
    doi:10.1016/j.na.2018.01.016     arXiv:1710.01974 [math.AP]

  32. L. Scarpa.
    Well-posedness for a class of doubly nonlinear stochastic PDEs of divergence type.
    J. Differential Equations 263 (2017), no. 4, 2113-2156.
    doi:10.1016/j.jde.2017.03.041     arXiv:1611.06790 [math.AP]

  33. P. Colli and L. Scarpa.
    From the viscous Cahn-Hilliard equation to a regularized forward-backward parabolic equation.
    Asympt. Anal. 99 (2016), no. 3-4, 183-205.
    doi:10.3233/ASY-161380     arXiv:1605.03857 [math.AP]

  34. P. Colli and L. Scarpa.
    Existence of solutions for a model of microwave heating.
    Discrete Contin. Dyn. Syst. Ser. A 36 (2016), no. 6, 3011-3034.
    doi:10.3934/dcds.2016.36.3011     arXiv:1505.03280 [math.AP]

  35. L. Scarpa.
    A doubly nonlinear evolution problem related to a model for microwave heating.
    Adv. Math. Sci. Appl. 24 (2014), no. 2, 251-275.
    arXiv:1411.7617 [math.AP]