Nichtlineare Analysis

  1. Universität
  2. Fakultäten
  3. Mathematisch-Naturwissenschaftlich-Technische Fakultät
  4. Institut für Mathematik
  5. Lehrstühle
  6. Nichtlineare Analysis
  7. Prof. Dr. Bernd Schmidt
  8. Publications of Bernd Schmidt

Publications of Bernd Schmidt

  • (with I. Giannoulis, G. Schneider) NLS approximation for a scalar FPUT system on a 2D square lattice with a cubic nonlinearity. Online preprint arXiv:2401.14947 [math.DS], 2024. [Preprint]
     

  • Most likely balls in Banach spaces: existence and non-existence. Online preprint arXiv:2309.02846 [math.FA], 2023. To appear in Bull. Lond. Math. Soc. (2024). [Preprint]
     

  • (with M. Steinbach) On discrete groups of Euclidean isometries: representation theory, harmonic analysis and splitting properties. J. Fourier Anal. Appl. 29 (2023), Paper No. 70, 39 pp. [Article]
     

  • (with J. Zeman) A continuum model for brittle nanowires derived from an atomistic description by Γ-convergence. Calc. Var. Partial Diff. Eq. 62 (2023), Art. 243, 37 pp. [Article]
     

  • (with J. Zeman) A bending-torsion theory for thin and ultrathin rods as a Γ-limit of atomistic models. SIAM Mult. Model. Simul. 21 (2023) pp. 1717-1745. ArXive
     

  • (with M. Santilli) Two-phase models for elastic membranes with soft inclusions. Rend. Lincei Mat. Appl. 34 (2023) pp. 401-431.  [Article]
     

  • (with M. Santilli) A Blake-Zisserman-Kirchhoff theory for plates with soft inclusions. J. Math. Pures Appl. 175 (2023), pp. 143-180. ArXive

     

  • (with T. Ruf) Unique minimizers and the representation of convex envelopes in locally convex vector spaces. J. Convex Anal. 29 (2022) pp. 929-937. ArXive

     

  • (with M. Steinbach) Stability of Objective Structures: General Criteria and Applications. Online preprint arXiv:2205.04849 [math.AP], 2022. ArXive

     

  • (with M. Steinbach) Korn type Inequalities for Objective Structures. Online preprint arXiv:2205.04840 [math.AP], 2022.  ArXive

     

  • (with V. Auer-Volkmann, L. Beck) Eigendamage: an Eigendeformation model for the variational approximation of cohesive fracture—a one-dimensional case study. Ann. Mat. Pura Appl. 201 (2022) pp. 2161-2195. [Article]

     

  • (with J. Braun) An atomistic derivation of von-Kármán plate theory. Netw. Heterog. Media 17 (2022), 613-644. [Artikel]
     

  • (with L. Kreutz, M. Friedrich) Emergence of rigid polycrystals from atomistic systems with Heitmann-Radin sticky disk energy. Arch. Ration. Mech. Anal. 240 (2021) pp. 627-698. [Article]
     

  • (with S. Jansen, W. König, F. Theil) Distribution of Cracks in a Chain of Atoms at Low Temperature. Ann Henri Poincaré 22 (2021) pp. 4131-4172. [Article]

     

  • (with S. Jansen, W. König, F. Theil) Surface energy and boundary layers for a chain of atoms at low temperature. Arch. Ration. Mech. Anal. 239 (2021) pp. 915–980. [Article]
     

  • (with M. Jesenko) Geometric linearization of theories for incompressible elastic materials and applications. Math. Models Methods Appl. Sci. 31 (2021) pp. 829-860. [Preprint]

     

  • (with M. de Benito Delgado) A hierarchy of multilayered plate models. ESAIM Control Optim. Calc. Var. 27 (2021), suppl., Paper No. S16, 35 pp. [Article] 

     

  • Effektive Theorien und Energie minimierende Konfigurationen für heterogene Schichten. In: GAMM-Rundbrief 2020/Heft 1, pp. 4-10. [Article]
     

  • (with E. Mainini) Maximal fluctuations around the Wulff shape for edge-isoperimetric sets in Zd: a sharp scaling law. Comm. Math. Phys. 380 (2020) pp. 947-971. [Article]
     

  • (with M. de Benito Delgado) Energy minimising configurations of pre-strained multilayers. J. Elasticity 140 (2020) pp. 303-335. [Article]
     

  • ´(with P. Piovano, E. Mainini, U. Stefanelli) N3/4 law in the cubic lattice. J. Stat. Phys. 176 (2019) pp. 1480-1499. [Artikel]
     
  • (with M. Ortiz, U. Stefanelli) A variational approach to Navier-Stokes. Nonlinearity 31 (2018) pp. 5664-5682. [Article]
     
  • (with M. Jesenko) Homogenization and the limit of vanishing hardening in Hencky plasticity with non-convex potentials. Calc. Var. Partial Diff. Eq. 57 (2018), Art. 2, 43 pp. [Article]
     
  • A Griffith-Euler-Bernoulli theory for thin brittle beams derived from nonlinear models in variational fracture mechanics. Math. Models Methods Appl. Sci. (M3AS) 27 (2017) pp. 1685-1726. [Article]
     
  • (with J. Braun) Existence and convergence of solutions of the boundary value problem in atomistic and continuum nonlinear elasticity theory. Calc. Var. Partial Diff. Eq. 55 (2016), Art. 125, 36 pp. [Article]
     
  • (with M. Friedrich) A quantitative geometric rigidity result in SBD. Online preprint arXiv:1503.06821 [math.AP], 2022. [Preprint]
     
  • (with M. Friedrich) 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. [Article]
     
  • (with M. Friedrich) An analysis of crystal cleavage in the passage from atomistic models to continuum theory. Arch. Ration. Mech. Anal. 217 (2015) pp. 263-308. [Article]
     
  • (with M. Jesenko) Closure and commutability results for Gamma-limits and the geometric linearization and homogenization of multi-well energy functionals. SIAM J. Math. Anal. 46 (2014) pp. 2525-2553. [Article]
     
  • On the infinite particle limit in Lagrangian dynamics and convergence of optimal transportation meshfree methods. SIAM Mult. Model. Simul. 12 (2014) pp. 265-289. [Article]
     
  • (with M. Friedrich) An atomistic-to-continuum analysis of crystal cleavage in a two-dimensional model problem. J. Nonlin. Sci. 24 (2014) pp. 145-183. [Article]
     
  • (with J. Braun) On the passage from atomistic systems to nonlinear elasticity theory for general multi-body potentials with p-growth. Netw. Heterog. Media 8 (2013) pp. 879-912. [Article]
     
  • Ground states of the 2D sticky disc model: fine properties and N3/4 law for the deviation from the asymptotic Wulff shape. J. Stat. Phys. 153 (2013) pp. 727-738. [Article]
     
  • (with A. Bompadre, M. Ortiz) Convergence Analysis of Meshfree Approximation Schemes. SIAM J. Numer. Anal. 50 (2012) pp. 1344-1366. [Article]
     
  • (with Y. Au Yeung, G. Friesecke) Minimizing atomic configurations of short range pair potentials in two dimensions: crystallization in the Wulff shape. Calc. Var. Partial Diff. Eq. 44 (2012) pp. 81-100. [Article]
     
  • (with F. Fraternali) Universal formulae for the limiting elastic energy of static membrane networks. J. Mech. Phys. Solids 60 (2012) pp. 172-180. [Article]
     
  • Localized spectral asymptotics for boundary value problems and correlation effects in the free Fermi gas in general domains. J. Math. Phys. 52 (2011) p. 072106 (18 pp.). [Article]
     
  • On a semilinear variational problem. ESAIM Control Optim. Calc. Var. 17 (2011) pp. 86-101. [Article]
     
  • (with M. Gonzalez, M. Ortiz) Force-stepping integrators in Lagrangian mechanics. Internat. J. Numer. Methods Engrg. 84 (2010) pp. 1407-1450. [Article]
     
  • (with G. Friesecke) A sharp version of Ehrenfest's theorem for general self-adjoint operators. Proc. R. Soc. Lond. Ser. A. 466 (2010) pp. 2137-2143. [Article]
     
  • (with M. Gonzalez, M. Ortiz) Energy-stepping integrators in Lagrangian mechanics. Internat. J. Numer. Methods Engrg. 82 (2010) pp. 205-241. [Article]
     
  • On the derivation of linear elasticity from atomistic models. Netw. Heterog. Media 4 (2009) pp. 789-812. [Article]
     
  • (with F. Fraternali, M. Ortiz) Eigenfracture: an eigendeformation approach to variational fracture. SIAM Mult. Model. Simul. 7 (2009) pp. 1237-1266. [Article]
     
  • (with S. Leyendecker, M. Ortiz) Gamma-convergence of variational integrators for constrained systems. J. Nonlin. Sci. 19 (2009) pp. 153-177. [Article]
     
  • (with A. Schlömerkemper) Discrete-to-continuum limit of magnetic forces: dependence on the distance between bodies. Arch. Ration. Mech. Anal. 192 (2009) pp. 689-611. [Article]
     
  • Linear Gamma-limits of multiwell energies in nonlinear elasticity theory. Contin. Mech. Thermodyn. 20 (2008) pp. 375-396. [Article]
     
  • Qualitative properties of a continuum theory for thin films. Annales de l'I.H.P. - Analyse non linéaire 25 (2008) pp. 43-75. [Article]
     
  • On the passage from atomic to continuum theory for thin films. Arch. Ration. Mech. Anal. 190 (2008) pp. 1-55. [Article]
     
  • Plate theory for stressed heterogeneous multilayers of finite bending energy. J. Math. Pures Appl. 88 (2007) pp. 107-122. [Article]
     
  • Minimal energy configurations of strained multi-layers. Calc. Var. Partial Diff. Eq. 30 (2007) pp. 477-497. [Article]
     
  • A derivation of continuum nonlinear plate theory from atomistic models. SIAM Mult. Model. Simul. 5 (2006) pp. 664-694. [Article]
     
  • Effective theories for thin elastic films. PhD-Thesis, Universität Leipzig (2006). [Thesis]
     
  • (with W. Huisinga) Metastability and Dominant Eigenvalues of Transfer Operators. In 'Advances in Algorithms for Macromolecular Simulation', Lecture Notes in Computational Science and Engineering, Springer (2005). [Article]


 

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