Prof. Dr. Caterina Zeppieri

Topics in Mathematics Münster

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

$\bullet$ 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.

$\bullet$ 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.

$\bullet$ 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.