Research

Research interests in Calculus of Variations, Free Discontinuity problems, Mean-Field particle systems.

Applications to elasticity/failure phenomena and population dynamics.

Here is a complete list of publications in chronological order. See also the arXiv and cvgmt profile.

Published papers

1. S. Almi and M. Degiovanni, On degree theory for quasilinear elliptic equations with natural growth conditions, Recent Trends in Nonlinear Partial Differential Equations II: Stationary Problems, J. B. Serrin, E. L. Mitidieri and V. D. Radulescu eds., 1-20, Contemporary Mathematics, 595, Amer. Math. Soc., Providence, R.I., 2013.

2. S. Almi, G. Dal Maso, and R. Toader, Quasi-static crack growth in  hydraulic fracture, Nonlinear Anal., 109 (2014), pp. 301-318. [Preprint]

3. S. Almi, Energy release rate and quasi-static evolution via vanishing viscosity in a fracture model depending on the crack opening, ESAIM Control Optim. Calc. Var., 23 (2017), pp. 791-826. [Preprint]

4. S. Almi, G. Dal Maso, and R. Toader, A lower semicontinuity result for a free discontinuity functional with a boundary term, J. Math. Pures Appl. (9),  108 (2017), pp. 952-990. [Preprint]

5. S. Almi, Quasi-static hydraulic crack growth driven by Darcy's law, Adv. Calc. Var., 11 (2018), pp. 161-191. [Preprint]

6. S. Almi and I. Lucardesi, Energy release rate and stress intensity factors in planar elasticity in presence of smooth cracks, NoDEA Nonlinear Differential Equations Appl., 25 (2018), pp. 25-43. [Preprint]

7. S. Almi and S. Belz, Consistent finite-dimensional approximation of phase-field models of fracture, Ann. Mat. Pura Appl. (4), 198 (2019), pp. 1191-1225. [Preprint]

8. S. Almi, S. Belz, and M. Negri, Convergence of discrete and continuous unilateral flows for Ambrosio-Tortorelli energies and application to mechanics, ESAIM Math. Model. Numer. Anal., 53 (2019),  pp. 659-6997. [Preprint]

9. S. Almi and M. Negri, Analysis of staggered evolutions for nonlinear energies in phase field fracture, Arch. Ration. Mech. Anal., 236 (2020), pp. 189-252. [Preprint]

10. S. Almi, G. Lazzaroni, and I. Lucardesi, Crack growth by vanishing viscosity in planar elasticity,  Math. Eng., 2(1) (2020), pp. 141-173. [Preprint]

11. S. Almi, Irreversibility and alternate minimization in phase field fracture: a viscosity approach, Z. Angew. Math. Phys., 71 (2020), Paper n. 128. [Preprint]

12. S. Almi, M. Fornasier, and R. Huber, Data-driven evolutions of critical points, Foundations of Data Science, (2020). [Preprint]

13. S. Almi and U. Stefanelli, Topology optimization for incremental elastoplasticity: a phase-field approach, SIAM J. Control Optim., 59(1), pp. 339-364. [Preprint]

14. S. Almi, S. Belz, S. Micheletti, and S. Perotto, A dimension-reduction model for brittle fractures on thin shells with mesh adaptivity, Math. Models Methods Appl. Sci., 31 (2021), pp. 37-81. [Preprint]

15. S. Almi, M. Morandotti, and F. Solombrino, A multi-step Lagrangian scheme for spatially inhomogeneous evolutionary games, J. Evol. Equ., 21 (2021), pp. 2691-2733. [Preprint]

16. G. Albi, S. Almi, M. Morandotti, and F. Solombrino, Mean-field selective optimal control via transient leadership, Applied  Math. Optim., 85 (2022), article n. 9. [Preprint]

17. S. Almi and U. Stefanelli, Topology optimization for quasistatic elastoplasticity, ESAIM Control Optim. Calc. Var., 28 (2022), 47. [Preprint]

18. S. Almi, C. D'Eramo, M. Morandotti, and F. Solombrino, Mean-field limits for entropic multi-population dynamical systems, Milan J. Math., 91 (2023), pp. 175-212. [Preprint]

19. S. Almi, E. Davoli, and M. Friedrich, Non-interpenetration conditions in the passage from nonlinear to linearized Griffith fracture, J. Math. Pures Appl. (9), 175 (2023), pp. 1-36. [Preprint]

20. S. Almi, D. Reggiani, and F. Solombrino, Brittle membranes in finite elasticity, ZAMM, 103 (2023). [Preprint]

21. S. Almi, M. Morandotti, and F. Solombrino, Optimal control problems in transport dynamics with additive noise, J.Differential Equations, 373 (2023), pp. 1-47. [Preprint]

22. S. Almi and E. Tasso, Brittle fracture in linearly elastic plates, Proc. Roy. Soc. Edinburgh Sect. A, 153 (2023), pp. 68-103. [Preprint]

23. S. Almi and E. Tasso, A new proof of compactness in G(S)BD, Adv. Calc. Var., 16 (2023), pp. 637-650. [Preprint]

24. S. Almi, S. Krömer, and A. Molchanova, A new example for the Lavrentiev phenomenon in Nonlinear Elasticity, Z. Angew. Math. Phys., 75 (2024), article n. 2. [Preprint]

25. S. Almi, D. Reggiani, and F. Solombrino, Lower semicontinuity and relaxation for free discontinuity functionals with non-standard growth, Calc. Var. Partial Differential Equations, 63 (2024), article n. 24. [Preprint]

26. S. Almi, M. Caponi, M. Friedrich, and F. Solombrino, Geometric rigidity on Sobolev spaces with variable exponent and applications, NoDEA Nonlinear Differential Equations Appl., 32 (2025), article n. 12. [Preprint]

27. S. Almi, M. Caponi, M. Friedrich, and F. Solombrino, A fractional approach to strain-gradient plasticity: beyond core-radius of discrete dislocations,  Math. Ann., 391 (2025), pp. 4063-4115. [Preprint]

28. S. Almi, A. Molchanova, and M. Kruzik, Linearization in magnetoelasticity, Adv. Calc. Var., 18 (2025), pp. 577-591. [Preprint]

29. S. Almi, R. Durastanti, and F. Solombrino, A Pontryagin Maximum Principle for agent-based models with convex state space, ESAIM: Control Optim. Calc. Var., 31 (2025), article n. 37. [Preprint]

30. S. Almi and U. Stefanelli, Phase-field topology optimization with periodic microstructure, SIAM J. Control Optim., 63 (2025), pp. 1458-1484. [Preprint]

31. S. Almi and E. Tasso, Generalized bounded deformation in non-Euclidean settings, Indiana Univ. Math. J.,  74 (2025), pp. 1099-1152. [Preprint]

32. S. Almi, D. Reggiani, and F. Solombrino, Geometric rigidity for incompatible fields in the multi-well case and an application to strain-gradient plasticity, Nonlinear Anal., 264 (2026), 113998. [Preprint]

33. S. Almi and E. Tasso, A general criterion for jump set slicing and applications, J. Funct. Anal., 290 (2026), 111412. [Preprint]

34. S. Almi, R. Badal, M. Friedrich, and S. Schwarzacher, Thermo-elastodynamics of nonlinearly viscous solids, Calc. Var. Partial Differential Equations, 65 (2026). [Preprint]

35. S. Almi, E. Davoli, A. Kubin, and E. Tasso, On De Giorgi's Conjecture of Nonlocal approximations for free-discontinuity problems: The symmetric gradient case, Calc. Var. Partial Differential Equations, 65 (2026), article n. 160. [Preprint]

36. S. Almi, R. Durastanti, and F. Solombrino, Mean field first order optimality condition under low regularity of controls, accepted for publication on SIAM J. Control Optim., (2026). [Preprint]

Preprints

37. S. Almi, M. Fornasier, J. Klemenc, and A. Scagliotti, Balanced quasistatic evolutions of critical points in metric spaces, Preprint arXiv arxiv.org/abs/2506.09812, (2025). [Preprint]

38. S. Almi, R. Rossi, and G. Savaré, The superposition principle for the continuity equation with singular flux, Preprint arXiv arxiv.org/abs/2506.15333, (2025). [Preprint]

39. S. Almi, C. Leone, and G. Manzo, Gradient regularity for double-phase orthotropic functionals, Preprint arXiv arxiv.org/abs/2507.18474, (2025). [Preprint]

40. S. Almi, A. Baldi, M. Morandotti, and F. Solombrino, A general perspective on CBO methods with stochastic rate of information, Preprint arXiv arxiv.org/abs/2507.20029, (2025). [Preprint]

41. S. Almi, M. Caponi, M. Friedrich, and F. Solombrino, Riesz fractional gradient functionals defined on partitions: nonlocal-to-local variational limits, Preprint arXiv arxiv.org/abs/2510.04881, (2025). [Preprint]

42. S. Almi, A. F. Donnarumma, and M. Friedrich, Asymptotic analysis for heterogeneous elastic energies with material voids, Preprint arXiv arxiv.org/abs/2602.17374, (2026). [Preprint]

43. S. Almi, A. Kubin, and E. Tasso, Approximation of symmetric total variation on point clouds, Preprint arXiv arxiv.org/abs/2603.28172, (2026). [Preprint]