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).