@article {2014,
	title = {Second Order Asymptotic Development for the Anisotropic Cahn-Hilliard Functional},
	year = {2014},
	note = {This article is composed if 33 pages and recorded in PDF format},
	publisher = {SISSA},
	abstract = {The asymptotic behavior of an anisotropic Cahn-Hilliard functional with prescribed mass and Dirichlet boundary condition is studied when the parameter $\varepsilon$ that determines the width of the transition layers tends to zero. The  double-well potential is assumed to be even and equal to $|s-1|^\beta$ near $s=1$, with  $1<\beta<2$. The first order term  in the asymptotic development by $\Gamma$-convergence is well-known, and is related to a suitable anisotropic perimeter of the interface. Here it is shown that, under these assumptions, the second order term is zero, which gives an estimate on the rate of convergence of the minimum values.},
	keywords = {Gamma-convergence, Cahn-Hilliard functional, phase transitions},
	url = {http://hdl.handle.net/1963/7390},
	author = {Gianni Dal Maso and Irene Fonseca and Giovanni Leoni}
}
@article {2013,
	title = {Analytical validation of a continuum model for epitaxial growth with elasticity on vicinal surfaces},
	number = {Archive for Rational Mechanics and Analysis},
	year = {2013},
	publisher = {Springer},
	abstract = {In this paper it is shown existence of weak solutions of a variational inequality derived from the continuum model introduced by Xiang [7, formula (3.62)] (see also the work of Xiang and E [8] and Xu and Xiang [9]) to describe the self-organization of terraces and steps driven by misfit elasticity between a film and a substrate in heteroepitaxial
growth. This model is obtained as a continuum limit of discrete theories of Duport, Politi, and Villain [3] and Tersoff, Phang, Zhang, and Lagally[6].},
	keywords = {singular nonlinear parabolic equations, Hilbert transform, thin films},
	doi = {10.1007/s00205-014-0730-4},
	url = {http://hdl.handle.net/1963/7245},
	author = {Gianni Dal Maso and Irene Fonseca and Giovanni Leoni}
}
@article {2011,
	title = {Singular perturbation models in phase transitions for second order materials},
	journal = {Indiana Univ. Math. J. 60 (2011) 367-409},
	number = {SISSA;20/2010/M},
	year = {2011},
	publisher = {Indiana University},
	abstract = {A variational model proposed in the physics literature to describe the onset of pattern formation in two-component bilayer membranes and amphiphilic monolayers leads to the analysis of a Ginzburg-Landau type energy with a negative term depending on the first derivative of the phase function. Scaling arguments motivate the study of the family of second order singular perturbed energies Fe having a negative term depending on the first derivative of the phase function. Here, the asymptotic behavior of {Fe} is studied using G-convergence techniques. In particular, compactness results and an integral representation of the limit energy are obtained.},
	doi = {10.1512/iumj.2011.60.4346},
	url = {http://hdl.handle.net/1963/3858},
	author = {Milena Chermisi and Gianni Dal Maso and Irene Fonseca and Giovanni Leoni}
}
@article {2010,
	title = {Exact reconstruction of damaged color images using a total variation model},
	journal = {Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 1291-1331},
	year = {2010},
	publisher = {Elsevier},
	abstract = {In this paper the reconstruction of damaged piecewice constant color images is studied using a RGB total variation based model for colorization/inpainting. In particular, it is shown that when color is known in a uniformly distributed region, then reconstruction is possible with maximal fidelity.},
	doi = {10.1016/j.anihpc.2010.06.004},
	url = {http://hdl.handle.net/1963/4039},
	author = {Irene Fonseca and Giovanni Leoni and Francesco Maggi and Massimiliano Morini}
}
@article {2010,
	title = {Nonlocal character of the reduced theory of thin films with higher order perturbations},
	journal = {Adv. Calc. Var. 3 (2010) 287-319},
	number = {SISSA;57/2009/M},
	year = {2010},
	doi = {10.1515/ACV.2010.012, /July/2010},
	url = {http://hdl.handle.net/1963/3754},
	author = {Gianni Dal Maso and Irene Fonseca and Giovanni Leoni}
}
@article {2009,
	title = {A higher order model for image restoration: the one dimensional case},
	journal = {SIAM J. Math. Anal. 40 (2009) 2351-2391},
	number = {SISSA;66/2008/M},
	year = {2009},
	abstract = {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.},
	doi = {10.1137/070697823},
	url = {http://hdl.handle.net/1963/3174},
	author = {Gianni Dal Maso and Irene Fonseca and Giovanni Leoni and Massimiliano Morini}
}
@article {2007,
	title = {Equilibrium configurations of epitaxially strained crystalline films: existence and regularity results},
	journal = {Arch. Ration. Mech. Anal. 186 (2007) 477-537},
	year = {2007},
	abstract = {Strained epitaxial films grown on a relatively thick substrate are considered in the context of plane linear elasticity. The total free energy of the system is assumed to be the sum of the energy of the free surface of the film and the strain energy. Because of the lattice mismatch between film and substrate, flat configurations are in general energetically unfavorable and a corrugated or islanded morphology is the preferred growth mode of the strained film. After specifying the functional setup in which the existence problem can be properly framed, a study of the qualitative properties of the solutions is undertaken. New regularity results for volume-constrained local minimizers of the total free energy are established, leading, as a byproduct, to a rigorous proof of the zero-contact-angle condition between islands and wetting layers.},
	doi = {10.1007/s00205-007-0082-4},
	url = {http://hdl.handle.net/1963/2350},
	author = {Irene Fonseca and Nicola Fusco and Giovanni Leoni and Massimiliano Morini}
}
@article {2007,
	title = {Necessary and sufficient conditions for the chainrule in W1,1loc(RN;Rd) and BVloc(RN;Rd)},
	journal = {J. Eur. Math. Soc. (JEMS) 9 (2007) 219-252},
	year = {2007},
	abstract = {<p>In this paper we prove necessary and sufficient conditions for the validity of the classical chain rule in Sobolev spaces and in the space of functions of bounded variation.</p>},
	doi = {10.4171/JEMS/78},
	url = {http://hdl.handle.net/1963/2037},
	author = {Giovanni Leoni and Massimiliano Morini}
}
@article {2004,
	title = {Higher order quasiconvexity reduces to quasiconvexity},
	journal = {Arch. Ration. Mech. Anal. 171 (2004) 55-81},
	number = {SISSA;41/2003/M},
	year = {2004},
	publisher = {Springer},
	abstract = {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.},
	doi = {10.1007/s00205-003-0278-1},
	url = {http://hdl.handle.net/1963/2911},
	author = {Gianni Dal Maso and Irene Fonseca and Giovanni Leoni and Massimiliano Morini}
}
