Research Interests
$\bullet$ Calculus of variations.
$\bullet$ Elliptic differential equations.
$\bullet$ $\Gamma$-convergence and relaxation.
$\bullet$ Periodic and stochastic homogenisation.
$\bullet$ Free-discontinuity problems.
$\bullet$ Variational modelling in elasticity, plasticity, and fracture mechanics.
• Ansini, Nadia; Dal Maso, Gianni; Zeppieri, Caterina Ida New results on Γ-limits of integral functionals. Annales de l'Institut Henri Poincaré C. Analyse non linéaire Vol. 31, 2014, pp 185-202 online
• Ansini, Nadia; Zeppieri, Caterina Ida Asymptotic analysis of nonsymmetric linear operators via Γ-convergence. SIAM Journal on Mathematical Analysis Vol. 44 (3), 2012, pp 1617-1635 online
• Barchiesi, Marco; Lazzaroni, Giuliano; Zeppieri, Caterina Ida A bridging mechanism in the homogenisation of brittle composites with soft inclusions. SIAM Journal on Mathematical Analysis Vol. 48 (2), 2016 online
• Cagnetti, Filippo; Dal Maso, Gianni; Scardia, Lucia; Zeppieri, Caterina Ida Γ-convergence of free-discontinuity problems. Annales de l'Institut Henri Poincaré C. Analyse non linéaire Vol. 36 (4), 2019, pp 1035–1079 online
• Cagnetti, Filippo; Dal Maso, Gianni; Scardia, Lucia; Zeppieri, Caterina Ida Stochastic homogenisation of free-discontinuity problems. Archive for Rational Mechanics and Analysis Vol. 233 (2), 2019, pp 935–974 online
• Cagnetti, Filippo; Dal Maso, Gianni; Scardia, Lucia; Zeppieri, Caterina Ida A global method for deterministic and stochastic homogenisation in BV. Annals of PDE Vol. 8 (1), 2022, pp 8 online
• Cicalese, Marco; Spadaro, Emanuele Nunzio; Zeppieri, Caterina Ida Asymptotic analysis of a second-order singular perturbation model for phase transitions. Calculus of Variations and Partial Differential Equations Vol. 41 (1-2), 2011, pp 127-150 online
• Müller, Stefan; Scardia, Lucia; Zeppieri, Caterina Ida Geometric rigidity for incompatible fields and an application to strain-gradient plasticity. Indiana University Mathematics Journal Vol. 63 (5), 2014, pp 1365-1396 online
• Ruf, Matthias; Zeppieri, Caterina Ida Stochastic homogenization of degenerate integral functionals with linear growth. Calculus of Variations and Partial Differential Equations Vol. 62 (138), 2023 online
• Scardia, Lucia; Zeppieri, Caterina Ida Line-tension model for plasticity as the Γ-limit of a nonlinear dislocation energy. SIAM Journal on Mathematical Analysis Vol. 44 (4), 2012, pp 2372-2400 online
Recent Publications of Prof. Dr. Caterina Zeppieri
$\bullet $ Lucia Scardia, Konstantinos Zemas, and Caterina Ida Zeppieri. Homogenisation of nonlinear Dirichlet problems in randomly perforated domains under minimal assumptions on the size of perforations. Probability Theory and Related Fields, 192(1):471–544, June 2025. doi:10.1007/s00440-024-01320-1.
$\bullet $ Giuliano Lazzaroni, Piotr Wozniak, and Caterina Ida Zeppieri. Strong approximation of special functions of bounded variation functions with prescribed jump direction. Mathematische Nachrichten, 298(1):312–327, January 2025. doi:10.1002/mana.202300346.
$\bullet $ Annika Bach, Teresa Esposito, Roberta Marziani, and Caterina Ida Zeppieri. Gradient damage models for heterogeneous materials. SIAM Journal on Mathematical Analysis, 55(4):3567–3601, August 2023. doi:10.1137/22M1499145.
$\bullet $ Xavier Pellet, Lucia Scardia, and Caterina Ida Zeppieri. Stochastic homogenisation of free-discontinuity functionals in randomly perforated domains. Advances in Calculus of Variations, 17(3):643–671, August 2023. doi:10.1515/acv-2022-0052.
$\bullet $ Lucia Scardia, Konstantinos Zemas, and Caterina Ida Zeppieri. Homogenisation of nonlinear Dirichlet problems in randomly perforated domains under minimal assumptions on the size of perforations. arXiv e-prints, July 2023. arXiv:2307.11605.
$\bullet $ Annika Bach, Roberta Marziani, and Caterina Ida Zeppieri. Γ-convergence and stochastic homogenisation of singularly-perturbed elliptic functionals. Calculus of Variations and Partial Differential Equations, 62(7):199, July 2023. doi:10.1007/s00526-023-02540-4.
$\bullet $ Matthias Ruf and Caterina Ida Zeppieri. Stochastic homogenization of degenerate integral functionals with linear growth. Calculus of Variations and Partial Differential Equations, 62(4):138, April 2023. doi:10.1007/s00526-023-02476-9.
$\bullet $ Chiara D'Onofrio and Caterina Ida Zeppieri. Γ-convergence and stochastic homogenization of degenerate integral functionals in weighted Sobolev spaces. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 153(2):491–544, February 2023. doi:10.1017/prm.2022.3.
$\bullet $ Filippo Cagnetti, Gianni Dal Maso, Lucia Scardia, and Caterina Ida Zeppieri. A global method for deterministic and stochastic homogenisation in BV. Annals of PDE, 8(1):8, April 2022. doi:10.1007/s40818-022-00119-4.
$\bullet $ Annika Bach, Teresa Esposito, Roberta Marziani, and Caterina Ida Zeppieri. Interaction between oscillations and singular perturbations in a one-dimensional phase-field model. In Research in Mathematics of Materials Science, Association for Women in Mathematics Series, pages 3–31. Springer International Publishing, April 2022. doi:10.1007/978-3-031-04496-0_1.
$\bullet $ Marco Cicalese, Matteo Focardi, and Caterina Ida Zeppieri. Phase-field approximation of functionals defined on piecewise-rigid maps. Journal of Nonlinear Science, 31(5):Paper No. 78, 25, July 2021. doi:10.1007/s00332-021-09733-1.
$\bullet $ Annika Bach, Andrea Braides, and Caterina Ida Zeppieri. Quantitative analysis of finite-difference approximations of free-discontinuity problems. Interfaces and Free Boundaries, 22(3):317–381, September 2020. doi:10.4171/ifb/443.
$\bullet $ Xavier Pellet, Lucia Scardia, and Caterina Ida Zeppieri. Stochastic homogenisation of free-discontinuity functionals in random perforated domains. arXiv e-prints, February 2020. arXiv:2002.01389.
$\bullet $ Caterina Ida Zeppieri. Homogenisation of high-contrast brittle materials. Math. Eng., 2(1):174–202, January 2020. doi:10.3934/mine.2020009.
$\bullet $ Filippo Cagnetti, Gianni Dal Maso, Lucia Scardia, and Caterina Ida Zeppieri. Γ-convergence of free-discontinuity problems. Annales de L'Institut Henri Poincare Section (C) Non Linear Analysis, 36(4):1035–1079, July 2019. doi:10.1016/j.anihpc.2018.11.003.
$\bullet $ Filippo Cagnetti, Gianni Dal Maso, Lucia Scardia, and Caterina Ida Zeppieri. Stochastic homogenisation of free-discontinuity problems. Arch. Ration. Mech. An., 233(2):935–974, March 2019. doi:10.1007/s00205-019-01372-x.
$\bullet $ Xavier Pellet, Lucia Scardia, and Caterina Ida Zeppieri. Homogenization of high-contrast Mumford-Shah energies. SIAM J. Math. Anal., 51(3):1696–1729, January 2019. doi:10.1137/18m1189804.