Projects in Mathematics Muenster
Research Interests

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

Selected Publications of 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 Publications

$\bullet$ X. Pellet, L. Scardia, and C. I. Zeppieri. Stochastic homogenisation of free-discontinuity functionals in random perforated domains. arXiv e-prints, February 2020. arXiv:2002.01389.

$\bullet$ C. I. Zeppieri. Homogenisation of high-contrast brittle materials. Mathematics in Engineering, 2(1):174–202, January 2020. doi:10.3934/mine.2020009.

$\bullet$ F. Cagnetti, G. Dal Maso, L. Scardia, and C. I. 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.

$\bullet$ F. Cagnetti, G. D. Maso, L. Scardia, and C. I. Zeppieri. Stochastic homogenisation of free-discontinuity problems. Archive for Rational Mechanics and Analysis, 233(2):935–974, March 2019. doi:10.1007/s00205-019-01372-x.

$\bullet$ X. Pellet, L. Scardia, and C. I. Zeppieri. Homogenization of high-contrast Mumford-Shah energies. SIAM Journal on Mathematical Analysis, 51(3):1696–1729, January 2019. doi:10.1137/18m1189804.