Sergio Conti, Matteo Focardi and Flaviana Iurlano Existence of strong minimizers for the Griffith static fracture model in dimension two Ann. Inst. Henri Poincaré C, Anal. Non Linéaire, 36: 455-474 2019 10.1016/j.anihpc.2018.06.003
Mihaela Ifrim, Herbert Koch and Daniel Tataru Dispersive decay of small data solutions for the KdV equation 2019 https://arxiv.org/abs/1901.05934
2018
Anton Bovier, Dmitry Ioffe and Patrick Müller The hydrodynamics limit for local mean-field dynamics with unbounded spins 2018 https://arxiv.org/abs/1805.00641
Sergio Conti, Matteo Focardi and Flaviana Iurlano Which special functions of bounded deformation have bounded variation Proc. Roy. Soc. Edinb. A, 148: 33-50 2018 10.1017/S030821051700004X
Abstract: Functions of bounded deformation (BD) arise naturally in the study of fracture and damage in a geometrically linear context. They are related to functions of bounded variation (BV), but are less well understood. We discuss here the relation to BV under additional regularity assumptions, which may require the regular part of the strain to have higher integrability or the jump set to have finite area or the Cantor part to vanish. On the positive side, we prove that BD functions which are piecewise affine on a Caccioppoli partition are in GSBV, and we prove that $SBD^p$ functions are approximately continuous $H^n-1$-a.e. away from the jump set. On the negative side, we construct a function which is $BD$ but not in BV and has distributional strain consisting only of a jump part, and one which has a distributional strain consisting of only a Cantor part.
2017
Sergio Conti, Matteo Focardi and Flaviana Iurlano Integral representation for functionals defined on $SBD^p$ in dimension two Arch. Ration. Mech. Anal., 223(3): 1337--1374 2017 10.1007/s00205-016-1059-y
2016
Sergio Conti, Matteo Focardi and Flaviana Iurlano Phase field approximation of cohesive fracture models Annales de l'Institut Henri Poincar{\'e} / Analyse non lin{\'e}aire, 33: 1033-1067 2016 10.1016/j.anihpc.2015.02.001
Abstract: We obtain a cohesive fracture model as a $\Gamma$-limit of scalar damage models in which the elastic coefficient is computed from the damage variable $v$ through a function $f_k$ of the form $f_k(v)=min\{1,\varepsilon_k^{1/2} f(v)\}$, with $f$ diverging for $v$ close to the value describing undamaged material. The resulting fracture energy can be determined by solving a one-dimensional vectorial optimal profile problem. It is linear in the opening $s$ at small values of $s$ and has a finite limit as $s\to\infty$. If the function $f$ is allowed to depend on the index $k$, for specific choices we recover in the limit Dugdale's and Griffith's fracture models, and models with surface energy density having a power-law growth at small openings.
Sergio Conti, Matteo Focardi and Flaviana Iurlano Existence of minimizers for the 2d stationary Griffith fracture model C. R. Math. Acad. Sci. Paris, 354(11): 1055--1059 2016 10.1016/j.crma.2016.09.003
Sergio Conti, Matteo Focardi and Flaviana Iurlano Some recent results on the convergence of damage to fracture Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl., 27(1): 51--60 2016 10.4171/RLM/722