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.
Selected Publications of Prof. Dr. Caterina Zeppieri
$\bullet$ J. J. Bevan and C. I. Zeppieri. A simple sufficient condition for the quasiconvexity of elastic stored-energy functions in spaces which allow for cavitation. Calc. Var. Partial Differential Equations, 55(2):Art. 42, 25, 2016.
$\bullet$ M. Barchiesi, G. Lazzaroni, and C. I. Zeppieri. A bridging mechanism in the homogenization of brittle composites with soft inclusions. SIAM J. Math. Anal., 48(2):1178–1209, 2016.
$\bullet$ M. Burger, T. Esposito, and C. I. Zeppieri. Second-order edge-penalization in the Ambrosio- Tortorelli functional. Multiscale Model. Simul., 13(4):1354–1389, 2015.
$\bullet$ S. Müller, L. Scardia, and C. I. Zeppieri. Geometric rigidity for incompatible fields, and an application to strain-gradient plasticity. Indiana Univ. Math. J., 63(5):1365–1396, 2014.
$\bullet$ N. Ansini, G. Dal Maso, and C. I. Zeppieri. New results on $\Gamma$-limits of integral functionals. Ann. Inst. H. Poincaré Anal. Non Linéaire, 31(1):185–202, 2014.
$\bullet$ N. Ansini, G. Dal Maso, and C. I. Zeppieri. $\Gamma$-convergence and $H$-convergence of linear elliptic operators. J. Math. Pures Appl., 99(3):321–329, 2013.
$\bullet$ L. Scardia and C. I. Zeppieri. Line-tension model for plasticity as the $\Gamma$-limit of a nonlinear dislocation energy. SIAM J. Math. Anal., 44(4):2372–2400, 2012.
$\bullet$ N. Ansini and C. I. Zeppieri. Asymptotic analysis of nonsymmetric linear operators via $\Gamma$-convergence. SIAM J. Math. Anal., 44(3):1617–1635, 2012.
$\bullet$ M. Cicalese, E. N. Spadaro, and C. I. Zeppieri. Asymptotic analysis of a second-order singular perturbation model for phase transitions. Calc. Var. Partial Differential Equations, 41(1-2):127–150, 2011.
$\bullet$ N. Ansini, J.-F. Babadjian, and C. I. Zeppieri. The Neumann sieve problem and dimensional reduction: a multiscale approach. Math. Models Methods Appl. Sci., 17(5):681–735, 2007.
Current Cluster Publications of Prof. Dr. Caterina Zeppieri
$\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 $ 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 $ 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 $ 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 $ 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 $ Filippo Cagnetti, Gianni Dal Maso, Lucia Scardia, and Caterina Ida Zeppieri. A global method for deterministic and stochastic homogenisation in BV. Ann. PDE, 8(1):8, April 2022. doi:10.1007/s40818-022-00119-4.
$\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, pages 1–54, February 2022. doi:10.1017/prm.2022.3.
$\bullet $ Marco Cicalese, Matteo Focardi, and Caterina Ida Zeppieri. Phase-field approximation of functionals defined on piecewise-rigid maps. J. Nonlinear Sci., 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 Free Bound., 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.