# Publikationen

## List of publications:

### Preprints:

- (with W. Górny, U. Stefanelli)
*The ℓ1 double-bubble problem in three dimensions.*Submitted 2023. [Preprint] - (with M. Bresciani, C. Mora-Corral)
*Variational models with Eulerian-Lagrangian formulation allowing for material failure.*Submitted 2024. [Preprint] - (with C. Labourie, K. Stinson)
*Strong existence for free discontinuity problems in linear elasticity.*Submitted 2024. [Preprint] - (with J. Seutter)
*Atomistic-to-continuum convergence for quasi-static crack growth in brittle materials.*Submitted 2024. [Preprint] - (with A. F. Donnarumma)
*Stochastic homogenisation for functionals defined on asymptotically piecewise rigid functions.*Submitted 2023. [Preprint] - (with R. Badal, L. Machill)
*Derivation of a von Kármán plate theory for thermoviscoelastic solids.*Submitted 2023. [Preprint] - (with C. Labourie, K. Stinson)
*On regularity for Griffith almost-minimizers in the plane.*Submitted 2023. [Preprint] - (with W. Górny, U. Stefanelli)
*A characterization of ℓ1 double bubbles with general interface interaction.*Submitted 2023. [Preprint] - (with M. Seitz, U. Stefanelli)
*Discrete-to-continuum linearization in atomistic dynamics.*Submitted 2023. [Preprint] - (with S. Almi, M. Caponi, F. Solombrino)
*Geometric rigidity on Sobolev spaces with variable exponent and applications.*Submitted 2023. [Preprint] - (with L. Kreutz, K. Zemas)
*Geometric rigidity in variable domains and derivation of linearized models for elastic materials with free surfaces.*Submitted 2021. [Preprint]

### Publications:

- (with M. Seitz, U. Stefanelli)
*Nonlocal-to-local limit in linearized viscoelasticity.*Comm. Appl Ind. Math., to appear. [Preprint] - (with L. Kreutz, K. Zemas)
*Derivation of effective theories for thin 3D nonlinearly elastic rods with voids.*Math. Models Methods Appl. Sci. (M3AS), to appear. [Preprint, Article] - (with L. Kreutz)
*A proof of finite crystallization via stratification.*J. Stat. Phys. 190:199 (2023). [Preprint, Article] - (with W. Górny, U. Stefanelli)
*The double-bubble problem on the square lattice.*Interfaces Free Bound. 26 (2024) pp. 79-134. [Preprint, Article] - (with L. Machill)
*One-dimensional viscoelastic von Kármán theories derived from nonlinear thin-walled beams.*

Calc. Var. PDE 62:190 (2023). [Preprint, Article] - (with S. Almi, E. Davoli)
*Non-interpenetration conditions in the passage from nonlinear to linearized Griffith fracture.*J. Math. Pures Appl.175 (2023) pp. 1-36. [Preprint, Article] - (with L. Kreutz, K. Zemas)
*From atomistic systems to linearized continuum models for elastic materials with voids.*Nonlinearity 36 (2023) pp. 679-735. [Preprint, Article] - (with R. Badal, M. Kruzik)
*Nonlinear and Linearized Models in Thermoviscoelasticity.*Arch. Ration. Mech. Anal. 247: 5 (2023). [Preprint, Article] - (with R. Badal, J. Seutter)
*Existence of quasi-static crack evolution for atomistic systems.*Forces in mechanics 9 (2022), 100138. [Preprint, Article] - (with E. Davoli)
*Two-well linearization for solid-solid phase transitions.*J. Eur. Math. Soc. (JEMS), to appear. [Preprint, Article] - (with M. Seitz, U. Stefanelli)
*Tilings with nonflat squares: a characterization.*Milan Journal of Mathematics 90 (2022), pp. 131-175. [Preprint, Article] - (with M. Perugini, F. Solombrino)
*Gamma-convergence for free-discontinuity problems in linear elasticity: Homogenization and relaxation.*Indiana University Mathematics Journal, to appear. [Preprint, Article] - (with L. Machill)
*Derivation of a one-dimensional von Kármán theory for viscoelastic ribbons.*NoDEA Nonlinear Differential Equations Appl. 59:11 (2022). [Preprint, Article] - (with L. Bétermin, U. Stefanelli)
*Angle-rigidity for Z^2 configurations.*Nonlinearity 34 (2021), pp. 8392-8413. [Preprint, Article] - (with L. Bétermin, U. Stefanelli)
*Lattice ground states for Embedded-Atom Models in 2D and 3D.*Letters in Mathematical Physics 111:107 (2021). [Preprint, Article] - (with L. Kreutz, B. Schmidt)
*Emergence of rigid polycrystals from atomistic systems with Heitmann-Radin sticky disk energy.*Arch. Ration. Mech. Anal. 240 (2021), pp. 627-698. [Preprint, Article] - (with M. Perugini, F. Solombrino)
*Lower semicontinuity for functionals defined on piecewise rigid functions and on GSBD.*J. Funct. Anal. 280 (2021), 108929. [Preprint, Article] - (with M. Kruzik, U. Stefanelli)
*Equilibrium of immersed hyperelastic solids.*DCDS-S, to appear. [Preprint, Article] - (with V. Crismale, F. Solombrino)
*Integral representation for energies in linear elasticity with surface discontinuities.*Adv. Calc. Var. 15 (2022), pp. 705–733. [Preprint, Article] - (with M. Kruzik)
*Derivation of von Kármán plate theory in the framework of three-dimensional viscoelasticity.*Arch. Ration. Mech. Anal. 238 (2020), pp. 489-540. [Preprint, Article] - (with U. Stefanelli)
*Crystallization in a one-dimensional periodic landscape.*J. Stat.Phys. 179 (2020), pp. 485-501. [Preprint, Article] - (with V. Crismale)
*Equilibrium configurations for epitaxially strained films and material voids in three-dimensional linear elasticity.*Arch. Ration. Mech. Anal. 237 (2020), pp. 1041-1098. [Preprint, Article] - (with U. Stefanelli)
*Ripples in graphene: A variational approach.*Comm. Math. Phys. 379 (2020), pp. 915–954. [Preprint, Article] - (with F. Solombrino)
*Functionals defined on piecewise rigid functions: Integral representation and Γ-convergence.*Arch. Ration. Mech. Anal. 236 (2020), pp. 1325-1387. [Preprint, Article] - (with E. Davoli)
*Two-well rigidity and multidimensional sharp-interface limits for solid-solid phase transitions.*Calc. Var. PDE 59:44 (2020). [Preprint, Article] - (with L. Kreutz)
*Finite crystallization and Wulff shape emergence for ionic compounds in the square lattice.*Nonlinearity 33 (2020), pp. 1240-1296. [Preprint, Article] - (with M. Kruzik, J. Valdman)
*Numerical approximation of von Kármán viscoelastic plates.*DCDS-S, 14 (2021), pp. 299-319. [Preprint, Article] *Griffith energies as small strain limit of nonlinear models for nonsimple brittle materials.*Mathematics in Engineering, 2 (2020), pp. 75-100. [Preprint, Article]- (with L. Kreutz)
*Crystallization in the hexagonal lattice for ionic dimers.*Math. Models Methods Appl. Sci. (M3AS) 29 (2019), pp. 1853-1900. [Preprint, Article] *A compactness result in GSBV^p and applications to Γ-convergence for free discontinuity problems.*Calc. Var. PDE 58:86 (2019). [Preprint, Article]- (with E. Mainini, P. Piovano, U. Stefanelli)
*Characterization of optimal carbon nanotubes under stretching and validation of the Cauchy-Born rule.*Arch. Ration. Mech. Anal. 231 (2019), pp. 465-517. [Preprint, Article] *A piecewise Korn inequality in SBD and applications to embedding and density results.*SIAM J. Math. Anal. 50 (2018), pp. 3842-3918. [Preprint, Article]- (with U. Ludacka, M. R. A. Monazam, C. Rentenberger, U. Stefanelli, J. C. Meyer, J. Kotakoski)
*In situ control over graphene ripples and strain in the electron microscope.*npj 2D Materials and Applications 2: 25 (2018). [Article] - (with M. Kruzik)
*On the passage from nonlinear to linearized viscoelasticity.*SIAM J. Math. Anal. 50 (2018), pp. 4426-4456. [Preprint, Article] - (with U. Stefanelli)
*Graphene ground states.*Zeitschrift für angewandte Mathematik und Physik, June 2018, 69:70. [Preprint, Article] - (with F. Solombrino)
*Quasistatic crack growth in 2d-linearized elasticity.*Ann. Inst. H. Poincaré Anal. Non Linéaire 35 (2018) pp. 27-64. [Preprint, Article] *On a decomposition of regular domains into John domains with uniform constants.*ESAIM Control Optim. Calc. Var. 24 (2018), pp. 1541-1583. [Preprint, Article]*A Korn-type inequality in SBD for functions with small jump sets.*Math. Models Methods Appl. Sci. (M3AS) 27 (2017) pp. 2461-2484. [Preprint, Article]*A derivation of linearized Griffith energies from nonlinear models.*Arch. Ration. Mech. Anal. 225 (2017) pp. 425-467. [Preprint, Article]- (with P. Piovano, U. Stefanelli)
*The geometry of C60: A rigorous approach via Molecular Mechanics.*SIAM J. Appl. Math. 76 (2016) pp. 2009-2029. [Preprint, Article] - (with B. Schmidt)
*On a discrete-to-continuum convergence result for a two dimensional brittle material in the small displacement regime.*Netw. Heterog. Media 10 (2015) pp. 321-342. [Preprint, Article] - (with B. Schmidt)
*An analysis of crystal cleavage in the passage from atomistic models to continuum theory.*Arch. Ration. Mech. Anal. 217 (2015) pp. 263-308. [Preprint, Article] - (with B. Schmidt)
*An atomistic-to-continuum analysis of crystal cleavage in a two-dimensional model problem.*J. Nonlin. Sci. 24 (2014) pp. 145-183. [Preprint, Article]

### Other:

- (with E. Mainini, P. Piovano)
*Atomistic potentials and the Cauchy-Born rule for carbon nanotubes: a review.*Rendiconti Sem. Mat. Univ. Pol. Torino. [Preprint] - (with B. Schmidt)
*A quantitative geometric rigidity result in SBD.*Preprint 2015. [Preprint] *A Korn-Poincaré-type inequality for special functions of bounded deformation.*Preprint 2015. [Preprint]