Filippo Cagnetti
University of Sussex
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Featured researches published by Filippo Cagnetti.
Mathematical Models and Methods in Applied Sciences | 2008
Filippo Cagnetti
The existence of crack evolutions based on critical points of the energy functional is proved, in the case of a cohesive zone model with prescribed crack path. It turns out that evolutions of this type satisfy a maximum stress criterion for the crack initiation. With an explicit example, it is shown that evolutions based on the absolute minimization of the energy functional do not enjoy this property.
Journal of the European Mathematical Society | 2013
Marco Barchiesi; Filippo Cagnetti; Nicola Fusco
The isoperimetric inequality for Steiner symmetrization of any codimension is investigated and the equality cases are characterized. Moreover, a quantitative version of this inequality is proven for convex sets.
Siam Journal on Mathematical Analysis | 2011
Filippo Cagnetti; Diogo A. Gomes; Hung Tran
The adjoint method, introduced in [L. C. Evans, Arch. Ration. Mech. Anal., 197 (2010), pp. 1053–1088] and [H. V. Tran, Calc. Var. Partial Differential Equations, 41 (2011), pp. 301–319], is used to construct analogues to the Aubry–Mather measures for nonconvex Hamiltonians. More precisely, a general construction of probability measures, which in the convex setting agree with Mather measures, is provided. These measures may fail to be invariant under the Hamiltonian flow and a dissipation arises, which is described by a positive semidefinite matrix of Borel measures. However, in the case of uniformly quasiconvex Hamiltonians the dissipation vanishes, and as a consequence the invariance is guaranteed.
Mathematical Models and Methods in Applied Sciences | 2017
Marco Artina; Filippo Cagnetti; Massimo Fornasier; Francesco Solombrino
We introduce a novel constructive approach to define time evolution of critical points of an energy functional. Our procedure, which is different from other more established approaches based on viscosity approximations in infinite dimension, is prone to efficient and consistent numerical implementations, and allows for an existence proof under very general assumptions. We consider in particular rather nonsmooth and nonconvex energy functionals, provided the domain of the energy is finite dimensional. Nevertheless, in the infinite dimensional case study of a cohesive fracture model, we prove a consistency theorem of a discrete-to-continuum limit. We show that a quasistatic evolution can be indeed recovered as a limit of evolutions of critical points of finite dimensional discretizations of the energy, constructed according to our scheme. To illustrate the results, we provide several numerical experiments both in one and two dimensions. These agree with the crack initiation criterion, which states that a fracture appears only when the stress overcomes a certain threshold, depending on the material.
Analysis & PDE | 2014
Filippo Cagnetti; Maria Colombo; Guido De Philippis; Francesco Maggi
Characterization results for equality cases and for rigidity of equality cases in Steiners perimeter inequality are presented. (By rigidity, we mean the situation when all equality cases are vertical translations of the Steiner symmetral under consideration.) We achieve this through the introduction of a suitable measure-theoretic notion of connectedness and a fine analysis of barycenter functions for sets of finite perimeter having segments as orthogonal sections with respect to a hyperplane.
Journal of the European Mathematical Society | 2017
Filippo Cagnetti; Maria Colombo; Guido De Philippis; Francesco Maggi
We provide a geometric characterization of rigidity of equality cases in Ehrhards symmetrization inequality for Gaussian perimeter. This condition is formulated in terms of a new measure-theoretic notion of connectedness for Borel sets, inspired by Federers definition of indecomposable current.
Proceedings of the Royal Society of Edinburgh: Section A Mathematics | 2011
Filippo Cagnetti
The relation between quasi-convexity and k-quasiconvexity (k greater than or equal to 2) is investigated. It is shown that every smooth strictly k-quasi-convex integrand with p-growth at infinity, p > 1, is the restriction to kth-order symmetric tensors of a quasiconvex function with the same growth. When the smoothness condition is dropped, it is possible to prove an approximation result. As a consequence, lower semicontinuity results for kth-order variational problems are deduced as corollaries of well-known first-order theorems. This generalizes a previous work by Dal Maso et al., in which the case where k = 2 was treated.
Calculus of Variations and Partial Differential Equations | 2008
Filippo Cagnetti; Maria Giovanna Mora; Massimiliano Morini
ESAIM: Control, Optimisation and Calculus of Variations | 2013
Filippo Cagnetti; Diogo A. Gomes; Hung V. Tran
Annales De L Institut Henri Poincare-analyse Non Lineaire | 2015
Filippo Cagnetti; Diogo A. Gomes; Hiroyoshi Mitake; Hung V. Tran