Research
RESEARCH INTERESTS
My research interests range across different areas of mathematical analysis and calculus of variation. The main direction of investigations are represented by geometric measure theory problems such as partition problems and Cheeger problems, fracture and image denoising models, analysis of energies defined on graphs and point clouds. The common feature of all these topics is that they can be treated by exploiting a variational approach and the direct method of calculus of variation.
PUBLICATIONS
13. Asymptotic behavior of the Dirichlet energy on Poisson point clouds. Caroccia - Braides, Journal of Nonlinear Science 33.5 (2023): 80. https://doi.org/10.1007/s00332-023-09937-7
12. Isoperimetric sets and p-Cheeger sets are in bijection. Caroccia - Saracco, J Geom Anal 33, 129 (2023). https://doi.org/10.1007/s12220-022-01157-x
11. A Compactness Theorem for functions on Poisson point clouds. Caroccia, Nonlinear Analysis, 2022, 113032, ISSN 0362-546X, https://doi.org/10.1016/j.na.2022.113032
10. Dimensional lower bounds for contact surfaces of Cheeger sets. Caroccia - Ciani, Journal de Mathématiques Pures et Appliquées 157 (2022): 1-44, https://doi.org/10.1016/j.matpur.2021.11.010
9. On the Gamma convergence of functionals defined over pairs of measures and energy-measures. Caroccia - Cristoferi, Journal of Nonlinear Science (2020), https://doi.org/10.1007/s00332-020-09623-y
8. On the integral representation of variational functionals on BD. Caroccia - Focardi - Van Goethem, SIAM Journal on Mathematical Analysis 52.4 (2020): 4022-4067, https://doi.org/10.1137/19M1277564
7. Mumford – Shah functionals on graphs and their asymptotics. Caroccia - Chambolle - Slepcev, Nonlinearity, Volume 33, Number 8 - https://doi.org/10.1088/1361-6544/ab81ee
6. Damage-driven fracture with low-order potentials: asymptotic behavior and applications. Caroccia - Van Goethem, ESAIM: M2AN, 53 4 (2019) 1305-1350, https://doi.org/10.1051/m2an/2019024
5. Equilibria configurations for epitaxial crystal growth with adatoms. Caroccia - Cristoferi - Dietrich, Archive for Rational Mechanics and Analysis (2018): 1-54, http://doi.org/10.1007/s00205-018-1258-9.
4. The Cheeger N-problem in terms of BV functions. Caroccia - Littig, Journal of Convex Analysis, Volume 26, Number 1 (2019).
3. Cheeger N-clusters. Caroccia, Calculus of variation and Partial Differential Equation (2017) 56:30, https://doi.org/10.1007/s00526-017-1109-9
2. A sharp quantitative version of Hales’ isoperimetric honeycomb theorem. Caroccia, Maggi - Journal de Mathématiques Pures et Appliquées 106.5 (2016): 935-956, https://doi.org/10.1016/j.matpur.2016.03.017
1. A note on the stability of the Cheeger constant of N-gons. Caroccia, Neumayer - Journal of Convex Analysis, Volume 22, Number 4, pgg. 1207-1213 (2015)
PREPRINTS UNDER REVIEW
PH.D THESIS
On the isoperimetric properties of planar N-clusters. Ph.D Thesis Caroccia, arXiv, preprint arXiv:1601.07116 (2016).