Mathematical Analysis - Calculus of Variations and PDEs
- Applied Mathematics and Calculus of Variations
- Variational analysis of atomistic and continuous physical models, analysis of problems with multiple scales
- Homogenization and Gamma-convergence
- Time-discrete variational schemes (minimizing movements), geometric minimizing movements
- Quasi static limits, vanishing viscosity / vanishing inertia approximations, gradient flows / rate-independent systems
- Discrete finite difference approximations / non local approximations of functionals in Fracture Mechanics
- Nematic elastomers, nonlinear elasticity
- Partial regularity for minimizers of quasiconvex variational integrals / double phase problems / non standard growth / elliptic and parabolic systems
- Regularity of minimizers/almost minimizers of one-phase free boundary problems with non-standard growth
- Lower semicontinuity of integral functionals
- Anzellotti pairing and its generalizations
My research activity basically covers:
- evolution of physical systems driven by interfacial type energies in presence of dissipation, by coupling the minimizing movements scheme for geometric evolutions due to Almgren, Taylor and Wang and a discrete-to-continuum analysis via Gamma-convergence. This new approach has been recently introduced by Braides, Gelli and Novaga to study the motion of discrete interfaces of nearest neighbors interacting ferromagnetic systems;
- vanishing-viscosity limits of gradient flow systems, delayed bifurcation, multiscale analysis, Balanced Viscosity solutions, vanishing inertia and viscosity limits, variational approach via time-discrete minimization schemes (minimizing movements), Inertial Balanced Viscosity solutions for rate-independent systems;
- finite difference approximation of free-discontinuity energies, quantitative analysis, non-local approximations;
- relaxation of elastic energies related to nematic elastomers, non-standard growth.
- partial regularity for minimizers of variational integrals whose integrands are discontinuous with respect to the x variable and have general growth in the gradient Du; partial regularity for double phase problems with non standard growth.
- integral representation theorems and Gamma convergence for free-discontinuity problems with non standard growth (variable exponent/Orlicz setting)
- lower semicontinuity of surface integrals, GSBD
See also my profiles on Google Scholar and Researchgate
[1] G. Scilla, Variational problems with percolation: rigid spin systems. Adv. Math. Sci. Appl. 23 (2013), 187-207. (preprint)
[2] A. Braides and G. Scilla, Motion of discrete interfaces in periodic media. Interfaces Free Bound. 15 (2013), 451-476. (preprint)
[3] G. Scilla, Motion of discrete interfaces in low contrast periodic media. Netw. Heterog. Media 9 (2014), 169-189. (preprint)
[4] A. Braides and G. Scilla, Nucleation and backward motion of discrete interfaces. C. R. Acad. Sci. Paris (2013), Vol. 351, Issues 21-22, 803-806. (preprint)
[5] A. Barbagallo and G. Scilla, Stochastic weighted variational inequalities in non-pivot Hilbert spaces with applications to a transportation model, J. Math. Anal. Appl. 457 (2) (2018), 1118-1134. 10.1016/j.jmaa.2017.07.067
[6] G. Scilla and V. Vallocchia, Chirality transitions in frustrated ferromagnetic spin chains: a link with the gradient theory of phase transitions, J. Elasticity 132(2) (2018), 271-293 (preprint)
[7] G. Scilla and F. Solombrino. Delayed loss of stability in singularly perturbed finite-dimensional gradient flows, Asymptot. Anal. 110 (1-2) (2018), 1-19 (preprint)
[8] G. Scilla and F. Solombrino, Multiscale analysis of singularly perturbed finite dimensional gradient flows: the minimizing movement approach, Nonlinearity 31(11) (2018), 5036-5074. (preprint)
[9] G. Scilla and F. Solombrino, A variational approach to the quasistatic limit of viscous dynamic evolutions in finite dimension, J. Differential Equations 267 (2019), 6216-6264. (preprint)
[10] G. Scilla and B. Stroffolini, Relaxation of nonlinear elastic energies related to Orlicz-Sobolev nematic elastomers, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 31(2020), 349-389. (preprint)
[11] G. Scilla, Motion of discrete interfaces on the triangular lattice. Milan J. Math. 88(2) (2020), 315-346 (preprint)
[12] V. Crismale, G. Scilla and F. Solombrino, A derivation of Griffith functionals from discrete finite-difference models, Calc. Var. Partial Differential Equations 59:193 (2020). (preprint)
[13] G. Scilla and F. Solombrino, Non-local approximation of the Griffith functional, NoDea Nonlinear Differential Equations Appl. 28:17 (2021). (preprint)
[14] A. Braides, G. Scilla and A. Tribuzio, Nucleation and growth of lattice crystals, J. Nonlinear Sci. 31:97 (2021). (preprint)
[15] C. Goodrich, G. Scilla and B. Stroffolini, Partial regularity for minimizers of discontinuous quasiconvex integrals with general growth, Proc. Roy. Soc. Edinburgh Sect. A (2021), doi: 10.1017/prm.2021.53 (preprint)
[16] F. Farroni, G. Scilla and F. Solombrino, On some non-local approximation of nonisotropic Griffith-type functionals, Math. Eng. 4(4)(2022), 1-22 (preprint)
[17] G. Scilla and B. Stroffolini, Invertibility of Orlicz-Sobolev maps, In: Español, M.I., Lewicka, M., Scardia, L., Schlömerkemper, A. (eds) Research in Mathematics of Materials Science. Association for Women in Mathematics Series, vol 31. Springer, Cham. (2022) https://doi.org/10.1007/978-3-031-04496-0_13 , (preprint).
[18] F. Riva, G. Scilla and F. Solombrino, The notions of Inertial Balanced Viscosity and Inertial Virtual Viscosity solution for rate-independent systems, Adv. Calc. Var. (2022) https://doi.org/10.1515/acv-2021-0073 , (preprint)
[19] J. Ok, G. Scilla and B. Stroffolini, Boundary partial regularity for minimizers of discontinuous quasiconvex integrals with general growth, Comm. Pure Appl. Anal. 21(12)(2022), 4173-4214, http://dx.doi.org/10.3934/cpaa.2022140 (preprint)
[20] V. De Cicco and G. Scilla, Lower semicontinuity in GSBD for nonautonomous surface integrals, To appear on ESAIM:COCV 29:13 (2023), https://doi.org/10.1051/cocv/2023001 (preprint)
[21] G. Scilla and B. Stroffolini, Partial regularity for steady double phase fluids, Math. Eng. 5(5) (2023), 1-47, https://doi.org/10.3934/mine.2023088 (preprint)
[22] G. Scilla, F. Solombrino and B. Stroffolini, Integral representation and Gamma-convergence for free-discontinuity problems with p(x)-growth, Calculus of Variations and Partial Differential Equations 62 (2023), art. 213 (preprint)
[23] C. Leone, G. Scilla, F. Solombrino and A. Verde, Regularity of minimizers for free-discontinuity problems with p(x)-growth, ESAIM: Control, Optimisation and Calculus of Variations 29 (2023), art n. 78 (preprint)
[24] J. Ok, G. Scilla and B. Stroffolini, Regularity theory for parabolic systems with Uhlenbeck structure, Journal de Mathématiques Pures et Appliquées 182 (2024), 116-163 (preprint)
[25] J. Ok, G. Scilla and B. Stroffolini, Partial regularity for degenerate parabolic systems with general growth via caloric approximations, Calculus of Variations and Partial Differential Equations 63 (2024), art. n. 105 (preprint)
[26] F. Riva, G. Scilla and F. Solombrino, Inertial Balanced Viscosity (IBV) solutions to infinite-dimensional rate-independent systems, to appear on Journal of Functional Analysis (2025), (preprint)
[27] C. Leone, G. Scilla, F. Solombrino and A. Verde, Strong existence for free-discontinuity problems with non-standard growth, To appear on SIAM: Journal on Mathematical Analysis (2025), (preprint)
[28] J. Ok, G. Scilla and B. Stroffolini, Partial regularity for degenerate systems of double phase type, To appear on Journal of Differential Equations (2025), (preprint)
[29] G. Scilla, Variational motion of discrete interfaces (PhD Thesis, 2014). (PDF)
[30] G. E. Comi, V. De Cicco and G. Scilla: Beyond BV: new pairings and Gauss-Green formulas for measure fields with divergence measure, Preprint (2023), (preprint)
[31] C. Leone, G. Scilla, F. Solombrino and A. Verde, Lipschitz regularity of almost-minimizers in one-phase problems with generalized Orlicz growth, Preprint (2025), (preprint)