Publications

Papers are listed in reverse chronological order.

Submitted papers

1. P. Colli, S. Kurima, L. Scarpa. Nonlocal to local convergence of phase field systems with inertial term.
   arXiv:2402.12145 [math.AP]

2. M. Fritz, L. Scarpa. Analysis and computations of a stochastic Cahn-Hilliard model for tumor growth with chemotaxis and variable mobility.
   arXiv:2312.06288 [math.AP]

3. E. Davoli, E. Rocca, L. Scarpa, L. Trussardi. Local asymptotics and optimal control for a viscous Cahn-Hilliard-Reaction-Diffusion model for tumor growth.
   arXiv:2311.10457 [math.AP]

4. A. Di Primio, M. Grasselli, L. Scarpa. Stochastic Cahn-Hilliard and conserved Allen-Cahn equations with logarithmic potential and conservative noise.
   arXiv:2309.04261 [math.AP]

5. F. Bertacco, C. Orrieri, L. Scarpa. Weak uniqueness by noise for singular stochastic PDEs.
   arXiv:2308.01642 [math.PR]

Published and accepted papers

6. A. Di Primio, M. Grasselli, L. Scarpa.  A stochastic Allen-Cahn-Navier-Stokes system with singular potential.
   J. Differential Equations (to appear).
   arXiv:2205.10521 [math.AP]

7. M. Hutzenthaler, A. Jentzen, K. Pohl, A. Riekert, L. Scarpa. Convergence proof for stochastic gradient descent in the training of deep neural networks with ReLU activation for constant target functions.
   Electron. Res. Arch. (to appear).
   arXiv:2112.07369 [cs.LG]

8. A. Agosti, E. Rocca, L. Scarpa. Strict separation and numerical approximation for a non-local Cahn-Hilliard equation with single-well potential.
   Discr. Cont. Dyn. Syst. Ser. S 17 (2024), no. 1, 462-511.
   doi:10.3934/dcdss.2023213     arXiv:2306.15819 [math.AP]

9. L. Scarpa, M. Zanella. Degenerate Kolmogorov equations and ergodicity for the stochastic Allen-Cahn equation with logarithmic potential.
   Stoch. Partial Differ. Equ. Anal. Comput. (2023).
   doi:10.1007/s40072-022-00284-4     arXiv:2206.09724 [math.PR]

10. C. Orrieri, L. Scarpa.  A note on regularity and separation for the stochastic Allen-Cahn equation with logarithmic potential.
    Discr. Cont. Dyn. Syst. Ser. S 16 (2023), no. 12, 3837-3851.
    doi:10.3934/dcdss.2023168     arXiv:2305.16666 [math.PR]

11. L. Scarpa, U. Stefanelli. Rate-independent stochastic evolution equations: parametrized solutions.
    J. Funct. Anal. 285 (2023), no. 10, Paper No. 110102.
    doi:10.1016/j.jfa.2023.110102     arXiv:2109.15208 [math.AP]

12. L. Scarpa. and U. Stefanelli. Doubly nonlinear stochastic evolution equations II.
    Stoch. Partial Differ. Equ. Anal. Comput. 11 (2023), no. 1, 307-347.
    doi:10.1007/s40072-021-00229-3     arXiv:2009.08209 [math.AP]

13. M. Grasselli, L. Scarpa, A. Signori. On a phase field model for RNA-Protein dynamics.
    SIAM J. Math. Anal. 55 (2023), no. 1, 405-457.
    doi:10.1137/22M1483086     arXiv:2203.03258 [math.AP]

14. P. Colli, T. Fukao, L. Scarpa.  A Cahn-Hilliard system with forward-backward dynamic boundary condition and non-smooth potentials.
    J. Evol. Equ. 22 (2022), no. 4, Paper No. 89.
    doi:10.1007/s00028-022-00847-x     arXiv:2208.00664 [math.AP]

15. F. Bertacco, C. Orrieri, L. Scarpa. Random separation property for stochastic Allen-Cahn-type equations.
    Electron. J. Probab. 27 (2022), 1-32.
    doi:10.1214/22-EJP830     arXiv:2110.06544 [math.PR]

16. P. Colli, T. Fukao, L. Scarpa. The Cahn-Hilliard equation with forward-backward dynamic boundary condition via vanishing viscosity.
    SIAM J. Math. Anal. 54 (2022), no. 3, 3292-3315.
    doi:10.1137/21M142441X     arXiv:2106.01010 [math.AP]

17. 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. (2021), no. 13, 2643–2694.
    doi:10.1142/S0218202521500585     arXiv:2009.11159 [math.AP]

18. L. Scarpa, U. Stefanelli. The Energy-Dissipation Principle for stochastic parabolic equations.
    Adv. Math. Sci. Appl. 30 (2021), no. 2, 429–452.
    arXiv:2109.05882 [math.AP]

19. 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]

20. 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]

21. 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]

22. 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]

23. 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]

24. 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]

25. 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]

26. 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]

27. 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]

28. 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]

29. 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]

30. 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]

31. 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]

32. 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]

33. 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]

34. 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]

35. 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]

36. 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]

37. 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]

38. 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]

39. 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]

40. 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]

41. 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]

42. 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]

43. 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]

44. 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]

45. 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]

46. 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]

47. 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]

48. 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]

Proceedings and chapters

1. C. Marinelli and L. Scarpa. Well-posedness of monotone semilinear SPDEs with semimartingale noise.
   Séminaire de Probabilités LI, (C. Donati-Martin, A. Lejay, A. Rouault, eds.)
   Lecture Notes in Mathematics, Springer, Cham. (2022), no. 2301, 259-301.
   doi:10.1007/978-3-030-96409-2_9     arXiv:1805.07562 [math.PR]

2. C. Marinelli and L. Scarpa. On the positivity of local mild solutions to stochastic evolution equations.
   Geometry and Invariance in Stochastic Dynamics, (S. Ugolini, M. Fuhrman, E. Mastrogiacomo, P. Morando, B. Rüdiger, eds.)
   Springer International Publishing (2022), 231-245.
   doi:10.1007/978-3-030-87432-2_12     arXiv:1912.13259 [math.AP]

3. C. Marinelli and L. Scarpa. On the well-posedness of SPDEs with singular drift in divergence form.
   Stochastic Partial Differential Equations and Related Fields, (A. Eberle, M. Grothaus, W. Hoh, M. Kassmann, W. Stannat, and G. Trutnau, eds.)
   Springer International Publishing (2018), 225-235.
   doi:10.1007/978-3-319-74929-7_12     arXiv:1701.08326 [math.AP]