%0 Journal Article
%J Adv. Calc. Var. 3 (2010) 345-370
%D 2010
%T Homogenization of fiber reinforced brittle material: the intermediate case
%A Gianni Dal Maso
%A Caterina Ida Zeppieri
%X We derive a cohesive fracture model by homogenizing a periodic composite material whose microstructure is characterized by the presence of brittle inclusions in a reticulated unbreakable elastic structure.
%B Adv. Calc. Var. 3 (2010) 345-370
%I Walter de Gruyter
%G en_US
%U http://hdl.handle.net/1963/3607
%1 694
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-04-02T10:43:00Z\\r\\nNo. of bitstreams: 1\\r\\nDM-Zep.pdf: 294507 bytes, checksum: 5ba95ca12abb15953a564aeedf353087 (MD5)
%R 10.1515/ACV.2010.011
%0 Journal Article
%J SIAM J. Math. Anal. 40 (2009) 2351-2391
%D 2009
%T A higher order model for image restoration: the one dimensional case
%A Gianni Dal Maso
%A Irene Fonseca
%A Giovanni Leoni
%A Massimiliano Morini
%X The higher order total variation-based model for image restoration proposed by Chan, Marquina, and Mulet in [6] is analyzed in one dimension. A suitable functional framework in which the minimization problem is well posed is being proposed and it is proved analytically that the\\nhigher order regularizing term prevents the occurrence of the staircase effect. The generalized version of the model considered here includes, as particular cases, some curvature dependent functionals.
%B SIAM J. Math. Anal. 40 (2009) 2351-2391
%G en_US
%U http://hdl.handle.net/1963/3174
%1 1127
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-23T07:52:52Z\\nNo. of bitstreams: 1\\nDM-Fon-Leo-Mor-08-preprint.pdf: 336946 bytes, checksum: 32db893a2b928f559b6744296e1d4f2c (MD5)
%R 10.1137/070697823
%0 Journal Article
%J SIAM J. Math. Anal. 41 (2009) 1874-1889
%D 2009
%T Homogenization of fiber reinforced brittle materials: the extremal cases
%A Marco Barchiesi
%A Gianni Dal Maso
%X We analyze the behavior of a fragile material reinforced by a reticulated elastic unbreakable structure in the case of antiplane shear. The microscopic geometry of this material is described by means of two small parameters: the period $\\\\varepsilon$ of the grid and the ratio $\\\\delta$ between the thickness of the fibers and the period $\\\\varepsilon$. We show that the asymptotic behavior as $\\\\varepsilon\\\\to0^+$ and $\\\\delta\\\\to0^+$ depends dramatically on the relative size of these parameters. Indeed, in the two cases considered, i.e., $\\\\varepsilon\\\\ll\\\\delta$ and $\\\\varepsilon\\\\gg\\\\delta$, we obtain two different limit models: a perfectly elastic model and an elastic model with macroscopic cracks, respectively.
%B SIAM J. Math. Anal. 41 (2009) 1874-1889
%I SIAM
%G en_US
%U http://hdl.handle.net/1963/2705
%1 1396
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-08-13T12:57:01Z\\nNo. of bitstreams: 1\\nmicrofibre.pdf: 236545 bytes, checksum: 53ef9ce789d27bba7dcac550930f306b (MD5)
%0 Journal Article
%J Arch. Ration. Mech. Anal. 171 (2004) 55-81
%D 2004
%T Higher order quasiconvexity reduces to quasiconvexity
%A Gianni Dal Maso
%A Irene Fonseca
%A Giovanni Leoni
%A Massimiliano Morini
%X In this paper it is shown that higher order quasiconvex functions suitable in the variational treatment of problems involving second derivatives may be extended to the space of all matrices as classical quasiconvex functions. Precisely, it is proved that a smooth strictly 2-quasiconvex function with p-growth at infinity, p>1, is the restriction to symmetric matrices of a 1-quasiconvex function with the same growth. As a consequence, lower semicontinuity results for second-order variational problems are deduced as corollaries of well-known first order theorems.
%B Arch. Ration. Mech. Anal. 171 (2004) 55-81
%I Springer
%G en_US
%U http://hdl.handle.net/1963/2911
%1 1789
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-11T12:36:19Z\\nNo. of bitstreams: 1\\nmath.AP0305138.pdf: 272082 bytes, checksum: 245f93702444ac3eb1de7c86c1f83551 (MD5)
%R 10.1007/s00205-003-0278-1