Publications
1) A. Garroni, A Wiener estimate for relaxed Dirichlet problems in
dimension N≥2, Differential and
Integral Equations 8 (1995), 849-866.
2) G. Dal Maso,
A. Garroni, New results on the asymptotic behaviour
of the solutions of Dirichlet problems in perforated domains, Mathematical
Models and Methods in Applied Science 4 (1994), 373-407. pdf
(preprint)
3) A. Braides,
A.
Garroni, Homogenization of nonlinear media with stiff and soft
inclusions,
Mathematical
Models and Methods in Applied Sciences 5
(1995), 543-564. pdf
(preprint)
4) G. Buttazzo, G. Dal Maso,
A. Garroni, A. Malusa, On the relaxed
formulation
of some shape optimization problems, Advances in Mathematical
Sciences
and Applications
7 (1997), 1-24. pdf (preprint)
5) G. Dal Maso,
A. Garroni, The capacity method for asymptotic
Dirichlet
problems,
Asymptotic Analysis 15 (1997), 299-324. pdf (preprint)
6) J.
Casado Diaz, A. Garroni, Asymptotic behaviour of nonlinear
elliptic
systems on varying domains, SIAM J. Math. Anal.
31
(2000), 581-624. pdf (preprint)
7) G. Dal Maso,
A. Garroni, I.V. Skrypnik, Capacitary method for
monotone
operators, J. Anal. Math. 71 (1997), 263-313. pdf (preprint)
8) L.
Ambrosio, A.
Braides,
A. Garroni, Special functions with bounded variation and with weakly
differentiable
traces on the jump set, Nonlinear Diff. Equations Appl.
5
(1998), 219-243.
9) J. Casado Diaz, A. Garroni, A non homogeneous extra term for the
limit of nonlinear Dirichlet problems in perforated domains, in Homogenization
and applications to material sciences (Nice, 1995), 81-94, GAKUTO
Internat. Ser. Math. Sci. Appl., 9, Gakkotosho, Tokyo, 1995. pdf (preprint)
10) A. Braides, A.
Garroni, On the non-local approximation of free-discontinuity
problems,
Comm.
Partial Diff. Equat. 23 (1998), 817-829. pdf (preprint)
11) A. Braides, G.
Dal Maso, A. Garroni, Variational formulation of softening
phenomena
in fracture mechanics: the one-dimensional case,
Arch. Rational Mech. Anal.146 (1999), n.1 23-58. pdf (preprint)
12) A. Garroni, B.
Niethammer, Correctors and error estimates in the
homogenization of a Mullins-Sekerka problem
Ann. Inst. H. Poincare Anal.
Non Lineaire 19 (2002), no. 4, 371--393. pdf (preprint)
13) M. Flucher, A. Garroni, S. Müller,
Concetration of low energy
extremals: Identification of concentration points
Calc. Var. Partial
Differential Equations 14 (2002), no. 4, 483-516. pdf (preprint)
14) A. Garroni, V. Nesi,
M. Ponsiglione, Dielectric breakdown: optimal bounds, Proc. Royal
Soc.
London A 457 (2001), 2317-2335. pdf (preprint)
15) A. Garroni, S.
Müller, Concentration
phenomena for the volume functional in unbounded domains:
Identification
of concentration points
J. Funct. Anal. , 199 (2003), no. 2, 386--410.
pdf (preprint)
16) M. Amar, A. Garroni, Gamma
convergence of concentrations problems
with critical growth. Ann. Scuola Norm. Sup. Pisa V , 2
(2003), no. 1, 151-179.
pdf (preprint)
17) A. Garroni, R.V. Kohn, Some
three-dimensional problems related to
dielectric breakdown and polycrystal plasticity,
Proc. Royal Soc. London
A, 459 (2003),
2613-2625.
pdf (preprint)
18) A. Garroni, V. Nesi,
Rigidity
and lack of rigidity for solenoidal matrix fields, Proc. Royal
Soc.
London A, 460 (2004), no. 2046, 1789-1806.
pdf (preprint)
19) A. Briani, A. Garroni, F. Prinari, Homogenization
of L^\infty functionals, Mathematical Models and Methods in
Applied
Sciences, 14
(2004), no. 12, 1761-1784.
pdf (preprint)
20) A. Garroni, S.
Müller, Gamma-limit
of a phase field
model of dislocations, SIAM J. Math. Anal., 36 (2005), no. 6, 1943-1964. pdf (preprint)
21) A. Garroni, S.
Müller, A variational
model for dislocations in the line tension limit, Arch. Rational Mech. Anal., 181 (2006), no. 3, 535-578. pdf (preprint)
22) G. Francfort, A. Garroni, A variational
view of brittle damage
evolution, Arch. Rational Mech. Anal., 182 (2006), no. 1, 125–152.
pdf (preprint)
23) A. Garroni, M. Ponsiglione, F. Prinari, From
1-homogeneous supremal functionals to difference quotients: relaxation
and Γ-convergence. Calc. Var.
Partial Differential Equations, 27
(2006), no. 4, 397-420.
pdf (preprint)
24) N. Ansini, A. Garroni, Γ-convergence of
integral functionals on divergence free fields, ESAIM: COCV , 13 (2007), no.4, 809–828. pdf (preprint)
25) G. Dal Maso,
A. Garroni, Gradient
bounds
for minimizers of variational problems related to cohesive zone models
in fracture mechanics, Calc.
Var. Partial Differential Equations, , 31 (2008), no. 2, 137–145. pdf (preprint)
26) M. Focardi, A. Garroni: A 1D macroscopic phase field model for
dislocations and a second order Γ-limit, Multiscale Modeling and
Simulation, Vol. 6
(2007), no. 4, 1098–1124. pdf
(preprint)
27) A. Garroni, C. J. Larsen: Threshold-based quasi-static brittle
damage evolution, Arch. Rational Mech. Anal., Vol. 194 (2009), no. 2,
585-609. pdf (preprint)
28) A. Garroni, G. Leoni, M. Ponsiglione Gradient theory for plasticity
via homogenization of discrete dislocations,J. Eur. Math. Soc. Vol. 12 (2010) , pp. 1231–1266 pdf (preprint)
29) S. Cacace, A. Garroni: A multi-phase transition model for
dislocations with interfacial microstructure, Interfaces and Free
Boundaries, Vol. 11 (2009), no.
2, 291-316. pdf (preprint)
30) S. Conti, A. Garroni, S. Muller: Singular
kernels, multiscale decomposition of microstructure, and dislocation
models, Arch. Rational Mech. Anal., Vol. 199 (2011), no. 3, 779-819. pdf
(preprint)
31) L. Bertini, P. Butta`, A. Garroni: Boundary effects in the gradient
theory of phase transitions, SIAM of Mathematical Analysis, SIAM of Mathematical Analysis, 44 (2012), no. 2, 926– 945. pdf (preprint)
32) L. De Luca, A. Garroni, M. Ponsiglione: Γ-convergence analysis of
systems of edge dislocations: the self energy regime, Arch. Rational Mech. Anal., Vol. 206 (2012), no. 3, 885–910. pdf (preprint)
33) R. Alicandro, L. De Luca, A. Garroni, M. Ponsiglione: Metasta-
bility and dynamics of discrete topological singularities in two
dimensions: a Γ-convergence approach, Arch. Rational Mech. Anal., Vol.
214 (2014), no. 1, pp 269–330. pdf (preprint).
34) A. Braides, B. Cassano, A. Garroni, D. Sarrocco: Quasi-static
damage evolution and homogenization: a paradigmatic case of
non-commutability, Ann. Inst. H. Poincaré Anal. Non Linéaire,
online 2014. pdf (preprint)
35) S. Conti, A. Garroni, A. Massaccesi: Modeling of dislocations
and relax- ation of functionals on 1-currents with discrete
multiplicity, Calc. Var. Partial Differential Equations, Volume 54, n.
2 (2015), 1847-1874 pdf (preprint)
36) S. Conti, A. Garroni, M. Ortiz: The line-tension approximation as
the dilute limit of linear-elastic dislocations, Arch. Rational Mech.
Anal., to appear.
37) S. Conti, A. Garroni, S. Mu ̈ller: Dislocation microstructures and
strain-gradient plasticity with one active slip plane, J. Mech. Phys.
Solids Vol. 93 (2016), 240-251.
38) A. Garroni, M. Peletier, L. Scardia, P. Van Meurs: Boundary-layer
analysis of a pile-up of walls of edge dislocations at a lock,
Mathematical Models and Methods in Applied Sciences, Vol. 26, no. 14
(2016) 2735-2768.
39) R. Alicandro, L. De Luca, A. Garroni, M. Ponsiglione: Dynamics of
discrete screw dislocations on glide directions, J. Mech. Phys. Solids,
Vol. 92 (2016), 87-10
40) S. Conti, A. Garroni, S. Mu ̈ller: Homogenization of vector-valued
partition problems and dislocation cell structures in the plane, Boll.
Unione Mat. Ital. 10 (2017), no. 1, 3-17.
41) A. Braides, A. Garroni, M. Palombaro: Interfacial energies of
systems of chiral molecules, Multiscale Model. Simul. Vol. 14 (2016),
no. 3, 1037-1062.
42) A. Braides, A. Garroni, S. Conti: Density of polyhedral partitions,
Calc. Var. Partial Differential Equations, Vol. 56 (2017), no. 2, Art.
28, 10 pp.
43) R. Alicandro, L. De Luca, A. Garroni, M. Ponsiglione: Minimising
move- ments for the motion of discrete screw dislocations along glide
directions. Calc. Var. Partial Differential Equations Vol. 56 (2017),
no. 5, Art. 148, 19 pp
Preprint
P. Ariza, S. Conti, A. Garroni, M. Ortiz: Variational modeling of dislocations in crystals in the line-tension limit
On books
A. Garroni: Γ-convergence of concentration problems, in “Topics on
concentration phenomena and problems with multiple scales”, Lect. Notes
Unione Mat. Ital., Vol. 2, Springer, Berlin, 2006, 233–266. pdf (preprint)
Proceedings
and other pubblications
i) G. Dal Maso,
A. Garroni Capacity theory for non-symmetric elliptic
operators, Preprint SISSA (1993). pdf (preprint)
ii) L. Ambrosio, A. Braides, A. Garroni: Free Discontinuity Problems,
Proceedings of the International Conference “Nonlinear Differential
Equations” (Kiev, Aug. 21-27, 1995) in “Nonlinear boundary value
problems”, Vol. 7 (1997), 3-12. pdf (preprint)
iii) A. Garroni, G. Palatucci: A singular
perturbation result with a fractional norm, in “Variational
Problems in Materials Science”, Progress in Nonlinear Differential
Equations and Their Applications, Vol. 68, Birkhauser, 2006, 111-126. pdf (preprint)
iv) A. Garroni: Quasi-static evolution of damage, Oberwolfach Report
Vol. 1 (2004), 1576.
v) A. Garroni: Asymptotics of phase-field models of dislocations,
Oberwolfach Report Vol. 2 (2005).
vi) A. Garroni: Threshold-based quasi-static brittle damage evolution,
Oberwolfach Report Vol. 4 (2007).
vii) A. Garroni: Variational models for plasticity by homogenization of
discrete dislocations, Oberwolfach Report Vol. 4 (2007).
viii) A. Garroni: Metastability and dynamics of discrete topological
singularities via Gamma-convergence: Application to dislocations,
Oberwolfach Report (2013).