L. Ambrosio, A. Braides: Functionals defined on partitions of sets of finite perimeter, I: integral representation and $\Gamma$-convergence J. Math. Pures. Appl. Vol. 69, p. 285-305, 1990 L. Ambrosio, A. Braides: Functionals defined on partitions of sets of finite perimeter, II: semicontinuity, relaxation and homogenization J. Math. Pures. Appl. Vol. 69, p. 307-333, 1990 A. Braides: Almost periodic methods in the theory of homogenization Applicable Anal. Vol. 47, p. 259-277, 1992 A. Braides, A. Coscia: The interaction between bulk energy and surface energy in multiple integrals Proceedings of the Royal Society of Edinburgh: Section A Mathematics Vol. 124, p. 737-756, 1994 L. Ambrosio, A. Braides, A. Garroni: Special functions with bounded variation and with weakly differentiable traces on the jump set (partially unpublished manuscript) 1995 A. Braides, A. Defranceschi, E. Vitali: Homogenization of Free-Discontinuity Problems Arch. Rational Mech. Anal. Vol. 135, p. 297-356, 1996 A. Braides, V. Chiadō Piat: Integral representation results for functionals defined on $SBV (\Omega; R^m)$ J. Math. Pures Appl. Vol. 75, p. 595-626, 1996 L. Ambrosio, A. Braides: Energies in SBV and variational models in fracture mechanics. Homogenization and Applications to Material Sciences, (D. Cioranescu, A. Damlamian, P. Donato eds.) GAKUTO, Gakkotosho, Tokio, Japan (Paper in Volume) p. 1-22, 1997 A. Braides, A. Defranceschi, E. Vitali: A relaxation approach to Hencky's plasticity Applied Math. Optim. Vol. 35, p. 45-68, 1997 R. Alicandro, A. Braides, M. S. Gelli: Free-discontinuity problems generated by singular perturbation The Royal Soc. of Edinburgh Vol. 128A, p. 1115-1129, 1998 N. Ansini, A. Braides, V. Chiadō Piat: Homogenization of Periodic Multi-dimensional Structures Boll. Un. Mat. Ital. Vol. 8, N. 2-B, p. 735-758, 1999 R. Alicandro, A. Braides, J. Shah: Free-discontinuity problems via functionals involving the $L^1$-norm of the gradient and their approximations. Interfaces Free Bound. Vol. 1, p. 17-37, 1999 A. Braides, G. Dal Maso, A. Garroni: Variational formulation of softening phenomena in Fracture Mechanics: the one-dimensional case Arch. Rational Mech. Anal. Vol. 146, p. 23-58, 1999 A. Braides, I. Fonseca, G. A. Francfort: 3D-2D asymptotic analysis for inhomogeneous thin films Indiana univ. Math. J. Vol. 49, p. 1367-1404, 2000 N. Ansini, A. Braides: Homogenization of Oscillating Boundaries and Applications to Thin Films J. d'Analyse Mathématique Vol. 83, p. 151-182, 2001 N. Ansini, A. Braides: Separation of scales and almost-periodic effects in the asymptotic behaviour of perforated periodic media. Acta Appl. Math. Vol. 65, p. 59081, 2001 A. Braides, A. Malchiodi: Curvature theory of boundary phases: the two-dimensional case Interfaces and Free Boundary Vol. 4, p. 345-370, 2002 A. Braides, A. Defranceschi, E. Vitali: Relaxation of elastic energies with free discontinuities and constraints on the strain Ann. Scuola Norm. Sup. Pisa (V) Vol. 1, p. 275-317, 2002 A. Braides, G. Buttazzo, I. Fragalā: Riemannian approximation of Finsler metrics Asymptotic Anal. Vol. 31, N. 2, p. 177-187, 2002 A. Braides, M. S. Gelli: Limits of discrete systems with long-range interactions. J. Convex Anal. Vol. 9, p. 363-399, 2002 N. Ansini, A. Braides, V. Chiadō Piat: Interaction between homogenization and phase-transition processes. Proc. Steklov. Math. Inst. Vol. 236, p. 373-385, 2002 A. Braides, M. S. Gelli, M. Sigalotti: The passage from non-convex discrete systems to variational problems in Sobolev spaces: the one-dimensional case Proc. Steklov. Math. Inst. Vol. 236, p. 395-414, 2002 A. Braides: Discrete approximation of functionals with jumps and creases Conference `Homogenization and Multiple Scales', Naples, 2001. (Conference Proceeding) 2002 A. Braides, M. S. Gelli: Continuum limits of discrete systems without convexity hypotheses. Math. Mech. Solids Vol. 7, p. 41-66, 2002 A. Braides: Gamma-convergence for Beginners Oxford University Press, Oxford (Book) 2002 N. Ansini, A. Braides: Asymptotic analysis of periodically-perforated nonlinear media J. Math. Pures Appl. Vol. 81, p. 439-451, 2002 K. Bhattacharya, A. Braides: Thin films with many small cracks Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Vol. 458, p. 823-840, 2002 N. Ansini, A. Braides, V. Chiadō Piat: Gradient theory of phase transitions in composite media Proc. Royal Soc. Edinburgh A Vol. 133, p. 265-296, 2003 A. Braides, M. S. Gelli: The passage from discrete to continuous variational problems: a nonlinear homogenization process (Conference Proceeding) 2003 A. Braides, V. Chiadō Piat, A. Piatnitski: A variational approach to double-porosity problems Asymptotic Analysis Vol. 39, p. 281-308, 2004 A. Braides, G. A. Francfort: Bounds on the effective behavior of a square conducting lattice Proc. R. Soc. London A. Vol. 460, p. 1755-1769 , 2004 A. Braides, V. Chiadō Piat: Another brick in the wall (Conference Proceeding) 2005 R. Alicandro, A. Braides, M. Cicalese: $L^\infty$ energies on discontinuous functions Discrete and Continuous Dynamical Systems Vol. 12, p. 905-928, 2005 A. Braides: A handbook of $\Gamma$-convergence ((in Handbook of Differential Equations.Stationary Partial Differential Equations, Volume 3 (M. Chipot and P. Quittner, eds.) Elsevier 2006)) 2006 N. Ansini, A. Braides, V. Valente: Multi-scale analysis by $\Gamma$-convergence of a one-dimensional non-local functional related to a shell-membrane transition SIAM J. Math. Anal. Vol. 38, N. 3, p. 944-976, 2006 A. Braides, A. J. Lew, M. Ortiz: Effective cohesive behavior of layers of interatomic planes Archive Rational Mech. Anal. Vol. 180, p. 151-182, 2006 R. Alicandro, A. Braides, M. Cicalese: Phase and anti-phase boundaries in binary discrete systems: a variational viewpoint Networks and Heterogeneous Media Vol. 1, p. 85-107, 2006 A. Braides, V. Chiadō Piat: Topics on concentration phenomena and problems with multiple scales. Springer-Verlag, Berlin (book - editors) 2006 A. Braides, R. March: Approximation by $\Gamma$-convergence of a curvature-depending functional in Visual Reconstruction Comm. Pure Appl. Math. Vol. 59, N. 1, p. 71-121, 2006 A. Braides, M. Solci, E. Vitali: A derivation of linear elastic energies from pair-interaction atomistic systems Networks and Heterogeneous Media Vol. 2, p. 551-587, 2007 A. Braides, A. Chambolle, M. Solci: A relaxation result for energies defined on pairs set-function and applications ESAIM: COCV Vol. 13, p. 717-734, 2007 A. Braides, C. I. Zeppieri: A note on equi-integrability in dimension reduction problems Calc. Var. Partial Differential Equations Vol. 29, p. 231-238, 2007 A. Braides, A. Gloria: Exact bounds on the effective behaviour of a conducting `discrete' polycrystal Multiscale Modeling and Simulation Vol. 6, p. 1198-1216, 2007 A. Braides, M. Cicalese: Surface energies in nonconvex discrete systems Math. Mod. Meth. Appl. Sci. (M3AS) Vol. 17, p. 985-1037, 2007 A. Braides, M. Briane: Homogenization of non-linear variational problems with thin low-conducting layers Appl. Math. Optim. Vol. 55, p. 1-29, 2007 A. Braides, M. Maslennikov, L. Sigalotti: Homogenization by blow-up Applicable Anal. Vol. 87, p. 1341-1356, 2008 A. Braides, A. Piatnitski: Overall properties of a discrete membrane with randomly distributed defects Arch. Ration. Anal. Mech. Vol. 189, p. 301-323, 2008 A. Braides, L. Sigalotti: Asymptotic analysis of periodically-perforated nonlinear media at and close to the critical exponent Comptes Rendus Acad. Sci. Paris Vol. 346, p. 363 - 367, 2008 A. Braides, G. Riey: A variational model in Image Processing with focal points ESAIM: M2AN Vol. 42, p. 729-748, 2008 R. Alicandro, A. Braides, M. Cicalese: Continuum limits of discrete thin films with superlinear growth densities Calc. Var. Partial Diff. Eq. Vol. 33, p. 267-297, 2008 A. Braides, V. Chiadō Piat: Non convex homogenization problems for singular structures Netw. Heterog. Media Vol. 3, N. 3, p. 489 - 508 , 2008 A. Braides, L. Truskinovsky: Asymptotic expansions by $\Gamma$-convergence Cont. Mech. Therm. Vol. 20, p. 21-62, 2008 A. Braides, G. Riey, M. Solci: Homogenization of Penrose tilings C. R. Acad. Sci. Paris Vol. 347, p. 697-700, 2009 A. Braides, C. I. Zeppieri: Multiscale analysis of a prototypical model for the interaction between microstructure and surface energy Interfaces Free Bound. Vol. 11, N. 1, p. 61-118, 2009 A. Braides, M. Briane, J. Casado-Diaz: Homogenization of non-uniformly bounded periodic diffusion energies in dimension two Nonlinearity Vol. 22, N. 6, p. 1459-1480, 2009 A. Braides, M. S. Gelli, M. Novaga: Motion and pinning of discrete interfaces Arch. Ration. Anal. Mech. Vol. 95, p. 469-498, 2010 A. Braides, A. Defranceschi, E. Vitali: A compactness result for a second-order variational discrete model ESAIM: M2AN Vol. 46, p. 389 - 410, 2011 A. Braides, A. Causin, M. Solci: Interfacial energies on quasicrystals IMA J Appl Math 2011 A. Braides, M. Solci: Interfacial energies on Penrose lattices Math. Mod. Meth. Appl. Sci. (M3AS) Vol. 21, p. 1193-1210, 2011 A. Braides, L. Sigalotti: Models of defects in atomistic systems Calc. Var. Partial Diff. Eq. Vol. 41, p. 71-109, 2011 A. Braides, C. J. Larsen: $\Gamma$-convergence for stable states and local minimizers Ann. Scuola Norm. Sup. Pisa Vol. 10, p. 193-206, 2011 A. Braides, A. Piatnitski: Variational problems with percolation: dilute spin systems at zero temperature (the 2-dimensional case) (Unpublished manuscript) 2011 A. Braides, N. K. Yip: A quantitative description of mesh dependence for the discretization of singularly perturbed non-convex problems SIAM J. Numer Anal. Vol. 50, N. 4, p. 1883--1898, 2012 A. Braides, A. Piatnitski: Variational problems with percolation: dilute spin systems at zero temperature J. Stat. Phys. Vol. 149, p. 846-864, 2012 A. Braides, M. Solci: Multi-scale free-discontinuity problems with soft inclusions Boll. Unione Mat. Ital. Vol. 6, p. 29-51, 2013 A. Braides, A. Piatnitski: Homogenization of surface and length energies for spin systems J. Funct. Anal. Vol. 264, p. 1296-1328, 2013 A. Braides: Local minimization, variational evolution and $\Gamma$-convergence Lecture Notes in Mathematics, Springer (Book) Vol. 2094, 2013 A. Braides, G. Scilla: Nucleation and backward motion of discrete interfaces C. R. Acad. Sci. Paris Vol. 351, N. 21-22, p. 803-806, 2013 A. Braides, M. Solci: Asymptotic analysis of atomistic systems with long-range interactions (Preprint) 2013 A. Braides, G. Scilla: Motion of discrete interfaces in periodic media Interfaces Free Bound. Vol. 15, N. 4, p. 451-476, 2013 A. Braides, A. Defranceschi, E. Vitali: Variational evolution of one-dimensional Lennard-Jones systems Netw. Heterog. Media Vol. 9, p. 217-238, 2014 A. Braides: An example of non-existence of plane-like minimizers for an almost-periodic Ising system J. Stat. Phys. Vol. 157, p. 295-302, 2014 A. Braides: Discrete-to-Continuum Variational Methods for Lattice Systems International Congress of Mathematicians (ICM 2014), Seoul, 2014 (Proceedings) 2014 A. Braides, M. Cicalese, F. Solombrino: Q-tensor continuum energies as limits of head-to-tail symmetric spins systems SIAM J. Math. Anal. Vol. 47, N. 4, p. 2832-2867 , 2015 A. Braides, V. Chiadō Piat, A. Piatnitski: Homogenization of Discrete High-Contrast Energies SIAM J. Math. Anal. Vol. 47, N. 4, p. 3064-3091, 2015 A. Braides, M. Colombo, M. Gobbino, M. Solci: Minimizing movements along a sequence of functionals and curves of maximal slope C. R. Acad. Sci. Paris, Ser. I Vol. 354, N. 7, p. 685-689, 2016 A. Braides, B. Cassano, A. Garroni, D. Sarrocco: Quasi-static damage evolution and homogenization: a case study of non-commutability Annales de l'Institut Henri Poincaré Vol. 303, p. 309-328, 2016 A. Braides, V. Chiadō Piat, M. Solci: Discrete double-porosity models for spin systems Math. Mech. Complex Syst. Vol. 4, p. 79-102, 2016 A. Braides, M. Solci: Motion of discrete interfaces through mushy layers J. Nonlinear Sci. Vol. 26, p. 1031-1053, 2016 A. Braides, M. S. Gelli: Asymptotic analysis of microscopic impenetrability constraints for atomistic systems J. Mech. Phys. Solids Vol. 96, p. 235-251, 2016 A. Braides, M. Cicalese, N. K. Yip: Crystalline Motion of Interfaces Between Patterns J. Stat. Phys. Vol. 165, N. 2, p. 274-319, 2016 A. Braides, A. Garroni, M. Palombaro: Interfacial energies of systems of chiral molecules Multiscale Model. Simul. Vol. 14, p. 1037-1062, 2016 A. Braides, M. Solci: Asymptotic analysis of Lennard-Jones systems beyond the nearest-neighbour setting: a one-dimensional prototypical case Math. Mech. Solids Vol. 21, p. 915-930, 2016 A. Braides, M. Cicalese: Interfaces, modulated phases and textures in lattice systems Arch. Ration. Mech. Anal. Vol. 223, p. 977-1017, 2017 A. Braides, A. Cancedda, V. Chiadō Piat: Homogenization of metrics in oscillating manifolds ESAIM: Control Optim. Calc. Var. Vol. 23, p. 889-912, 2017 A. Braides, A. Causin, M. Solci: Homogenization of interacting media (Preprint) 2017 A. Braides, M. S. Gelli: Analytical treatment for the asymptotic analysis of microscopic impenetrability constraints for atomistic systems ESAIM: M2AN Vol. 51, p. 1903-1929, 2017 A. Braides, L. Kreutz: Optimal bounds for periodic mixtures of nearest-neighbour ferromagnetic interactions Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. Vol. 28, p. 103-117, 2017 A. Braides, S. Conti, A. Garroni: Density of polyhedral partitions Calc. Var. Partial Diff. Equations Vol. 56, N. 2, p. 10, 2017 A. Braides, M. Cicalese, M. Ruf: Continuum limit and stochastic homogenization of discrete ferromagnetic thin films Analysis & PDE Vol. 11, N. 2, p. 499-553, 2018 A. Braides, A. Causin, M. Solci: Asymptotic analysis of a ferromagnetic Ising system with "diffuse" interfacial energy Ann.Mat.Pura Appl Vol. 197, N. 2, p. 583-604, 2018 A. Braides: Rigidity effects for antiferromagnetic thin films: a prototypical example (Book Chapter- Trends in Applications of Mathematics to Mechanics (E.Rocca et al, eds) Springer) 2018 A. Braides, L. Kreutz: Design of lattice surface energies Calc. Var. Partial Diff. Equations Vol. 57, 2018 A. Braides, V. Vallocchia: Static, Quasi-static and Dynamic Analysis for Scaled Perona-Malik Functionals Acta Applicandae Mathematicae Vol. 156, p. 79-107, 2018 A. Braides, L. Kreutz: An integral-representation result for continuum limits of discrete energies with multi-body interactions SIAM J. Math. Anal. Vol. 50, p. 1485-1520, 2018 A. Braides, A. Causin, A. Piatnitski, M. Solci: Asymptotic behaviour of ground states for mixtures of ferromagnetic and antiferromagnetic interactions in a dilute regime J. Stat. Phys. Vol. 171, p. 1096-1111, 2018 A. Braides, A. Causin, M. Solci: A homogenization result for interacting elastic and brittle media Proceedings A. Roy. Soc. London Vol. 474, 2018 A. Braides, V. Chiadō Piat: Homogenization of networks in domains with oscillating boundaries Applicable Analysis Vol. 98, p. 45-63, 2019 N. Ansini, A. Braides, J. Zimmer: Minimising movements for oscillating energies: the critical regime Proc. Roy. Soc. Edinburgh A Vol. 149, p. 719-737, 2019 A. Braides, V. Vallocchia: Two geometric lemmas for $S^{N-1}$-valued maps and an application to the homogenization of spin systems COCV Vol. 27, p. 13, 2020 A. Braides, N. A. Nodargi: Homogenization of cohesive fracture in masonry structures Math. Mech. Solids Vol. 28, p. 181-200, 2020 A. Braides, P. Cermelli, S. Dovetta: $\Gamma$-limit of the cut functional on dense graph sequences ESAIM: Control, Optimization and Calculus of Variations Vol. 26, 2020 A. Bach, A. Braides, C. I. Zeppieri: Quantitative analysis of finite-difference approximations of free-discontinuity problems Interfaces Free Bound. Vol. 22, 2020 A. Bach, A. Braides, M. Cicalese: Discrete-to-continuum limits of multi-body systems with bulk and surface long-range interactions SIAM J. Math. Anal. Vol. 52, p. 3600-2665, 2020 A. Braides, M. Solci: Compactness by coarse-graining in long-range lattice systems Adv. Nonlin. Studies Vol. 20, p. 783794, 2020 A. Braides, A. Malusa, M. Novaga: Crystalline evolutions with rapidly oscillating forcing terms Ann. Scuola Normale Sup.Pisa Vol. XX, N. 1, p. 143-175, 2020 A. Braides, V. Chiadō Piat, L. D'Elia: An extension theorem from connected sets and homogenization of non-local functionals Nonlinear Analysis Vol. 208, p. 112316, 2021 A. Braides, G. Scilla, A. Tribuzio: Nucleation and growth of lattice crystals J. Nonlinear Sci. Vol. 31, N. 97, 2021 A. Braides: Variational Problems on Networks (Lecture Notes) 2021 A. Braides, A. Piatnitski: Homogenization of random convolution energies J.London Math Soc. Vol. 104, p. 295-319, 2021 A. Braides, M. Solci: Geometric Flows on Planar Lattices Birkhäuser Pathways of Mathematics (Book) 2021 A. Braides, A. Tribuzio: Perturbed minimizing movements of families of functionals Discrete and Continuous Dynamical Systems Series S Vol. 14, N. 1, p. 373-393, 2021 A. Braides, A. Piatnitski: Homogenization of ferromagnetic energies on Poisson random sets in the plane Arch. Rational Mech. Anal. Vol. 243, p. 433-458, 2022 R. Alicandro, A. Braides, M. Cicalese, L. De Luca, A. Piatnitski: Topological singularities in periodic media: Ginzburg-Landau and core-radius approaches Arch. Ration. Mech. Anal. Vol. 243, p. 559-609, 2022 A. Braides, A. Piatnitski: Homogenization of quadratic convolution energies in periodically perforated domains Adv. Calc. Var. Vol. 15, p. 351-368, 2022 A. Braides, L. D'Elia: Homogenization of discrete thin structures Nonlinear Analysis Vol. 231, p. 112951, 2023 A. Braides, G. Dal Maso: Compactness for a class of integral functionals with interacting local and non-local terms Calc. Var. Partial Differential Equations Vol. 62, N. 148, 2023 A. Braides: A simplified counterexample to the integral representation of the relaxation of double integrals Comptes Rendus - Série Mathématique (Accepted Paper) 2023 A. Braides, M. Caroccia: Asymptotic behavior of the Dirichlet energy on Poisson point clouds J. Nonlinear Sci. Vol. 33, N. 80, 2023 I. Anello, A. Braides, F. Caragiulo: A note on the homogenization of incommensurate thin films Math. Meth. Appl. Sci. Vol. 46, p. 15655-15666, 2023 R. Alicandro, A. Braides, M. Solci, G. Stefani: Topological singularities arising from fractional-gradient energies (Submitted Paper) 2023 A. Braides, A. Chambolle: Ising systems, measures on the sphere, and zonoids Tunisian J. Math. (Accepted Paper) 2023 R. Alicandro, N. Ansini, A. Braides, A. Piatnitski, A. Tribuzio: A Variational Theory of Convolution-type Functionals SpringerBriefs on PDEs and Data Science (Book) p. 121, 2023 A. Braides, A. Causin, M. Solci: Discrete approximation of nonlocal-gradient energies Adv. Calc. Var. 2023 A. Braides, G. Dal Maso: Continuity of some non-local functionals with respect to a convergence of the underlying measures J. Math. Pures Appl. Vol. 170, p. 136--149, 2023 A. Braides, G. C. Brusca, D. Donati: Another look at elliptic homogenization Milan J. Math (Accepted Paper) 2023 A. Braides, G. C. Brusca: Asymptotic behaviour of the capacity in two-dimensional heterogeneous media Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Vol. 34, p. 383-399, 2023 A. Braides, A. Causin, M. Solci, L. Truskinovsky: Beyond the classical Cauchy-Born rule Archive for Rational Mechanics and Analysis Vol. 247, N. 107, 2023 R. Alicandro, A. Braides, M. Cicalese, M. Solci: Discrete Variational Problems with Interfaces Cambridge University Press (Book) 2023 A. Braides, G. Dal Maso: Validity and failure of the integral representation of -limits of convex non-local functionals J. Functional Anal. (Published Paper (on line)) 2024 A. Braides, G. Dal Maso, C. Le Bris: A closure theorem for $\Gamma$-convergence and H-convergence with applications to non-periodic homogenization (Submitted Paper) 2024