Mathias Schäffner

MLU Halle
Institut für Mathematik

email: firstname.schaeffner (at) mathematik.uni-halle.de
office: Room 1.38.0, Theodor-Lieser-Str. 5 06120 Halle (Saale) Germany

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Research interests

I am interested in Partial Differential Equations and Calculus of Variations, in particular I work on

• regularity theory for (non-uniformly) elliptic equations
• homogenization of elliptic equations and variational problems

Short CV

• Since 10/22: tenured position at MLU Halle
• 04/20 - 09/22: Junior Professor at TU Dortmund (non tenure-track)
• 10/18 - 03/20: Postdoc at U Leipzig / MPI Leipzig (mentor: Prof. Peter Bella, Felix Otto)
• 10/15 - 09/18: Postdoc at TU Dresden (mentor: Prof. Stefan Neukamm)
• 10/15: PhD in Mathematics at MLU Würzburg (supervisor: Prof. Anja Schlömerkemper)

Publications

Preprints

• Non-uniformly elliptic variational problems on BV.
  with Lisa Beck and Franz Gmeineder
  submitted (arXiv)
  
  
• Regularity for monotone Operators and applications to homogenization of p-Laplace type equations.
  with Lukas Koch
  submitted (arXiv)
  
  
• Mechanical behaviour of heterogeneous nanochains in the Gamma-limit of stochastic particle systems.
  with Laura Lauerbach, Stefan Neukamm and Anja Schlömerkemper
  preprint (arXiv)
  
  

published/accepted Articles

1. M. Ruf and M. Schäffner
   Upper bounds for the homogenization problem in nonlinear elasticity: the incompressible case.
   Calc. Var. Partial Differential Equations, 65 4 (2026) (arXiv) (Journal)
   
   
2. L. Koch, M. Ruf and M. Schäffner
   On the Lavrentiev gap for convex, vectorial integral functionals.
   J. Funct. Anal. 288 (2025), no. 5, Paper No. 110793. (arXiv) (Journal)
   
   
3. M. Schäffner
   Lipschitz bounds for nonuniformly elliptic integral functionals in the plane.
   Proc. Amer. Math. Soc. 152 no. 11 (2024), 4717-4727. (arXiv) (Journal)
   
   
4. M. Schäffner and B. Schweizer
   The time horizon for stochastic homogenization of the one-dimensional wave equation.
   Asymptotic Analysis 144 (1) (2025), 1143-1173. (preprint) (Journal)
   
   
5. A. Cianchi and M. Schäffner
   Local boundedness of minimizers under unbalanced Orlicz growth conditions.
   J. Differential Equations 401 (2024), 58-92. (arXiv) (Journal)
   
   
6. M. Josien, C. Raithel and M. Schäffner
   Stochastic homogenization and geometric singularities : a study on corners. SIAM J. Math. Anal., 56 (2024), no. 2, 1495-2455. (arXiv) (Journal)
   
   
7. S. Neukamm, M. Schäffner and M. Varga
   Quantitative stochastic homogenization of nonlinearly elastic, random laminates.
   Ann. Inst. H. Poincarè Anal. Non Linèaire, 43 (2025) no. 2, 331-390. (arXiv) (Journal)
   
   
8. M. Ruf and M. Schäffner
   New homogenization results for convex integral functionals and their Euler-Lagrange equations.
   Calc. Var. Partial Differential Equations, 63 32 (2024) (arXiv) (Journal)
   
   
9. M. Schäffner, B. Schweizer and Y. Tjandrawidjaja
   A radiation box domain truncation scheme for the wave equation.
   IMA J. Numer. Anal. 44 (2024) no. 2, 920-944. (Journal)
   
   
10. Local boundedness for p-Laplacian with degenerate coefficients.
    with Peter Bella
    Math. Eng., 5 (2023), no 5. (arXiv) (Journal)
    
    
11. Lipschitz bounds for integral functionals with (p,q)-growth conditions.
    with Peter Bella
    Adv. Calc. Var., 17 no. 2, (2024) 373-390. (arXiv) (Journal)
    
    
12. Domain truncation methods for the wave equation in a homogenization limit.
    with Ben Schweizer and Yohanes Tjandrawidjaja
    Appl. Anal. 101 (2022), no. 12, 4149--4170. (preprint) (Journal)
    
    
13. Non-uniformly parabolic equations and applications to the random conductance model.
    with Peter Bella
    Probab. Theory Related Fields. 182 (2022), no. 1-2, 353--397. (arXiv) (Journal)
    
    
14. Higher integrability for variational integrals with non-standard growth.
    Calc. Var. Partial Differential Equations 60 77 (2021) (arXiv) (Journal)
    
    
15. Growth conditions and regularity, an optimal local boundedness result.
    together with Jonas Hirsch
    Commun. Contemp. Math. 23, no. 3, 2050029 (2021). (arXiv) (Journal)
    
    
16. Local boundedness and Harnack inequality for solutions of linear non-uniformly elliptic equations.
    together with Peter Bella
    Comm. Pure Appl. Math. 74 (2021), no. 3, 453--477. (arXiv) ( Journal)
    
    
17. Derivation of a homogenized bending--torsion theory for rods with micro-heterogeneous prestrain.
    together with Robert Bauer and Stefan Neukamm
    J. Elast. 141, 109-145 2020. (arXiv) (Journal)
    
    
18. On the regularity of minimizers for scalar integral functionals with (p,q)-growth.
    together with Peter Bella
    Analysis and PDE 13 2020, no. 7, 2241-2257. (arXiv) (Journal)
    
    
19. Quenched invariance principle for random walks among random degenerate conductances.
    together with Peter Bella
    Ann. Probab. 48 (2020), no. 1, 296-316. (arXiv) (Journal)
    
    
20. Lipschitz estimates and existence of correctors for nonlinearly elastic, periodic composites subject to small strains.
    together with Stefan Neukamm
    Calc. Var. Partial Differential Equations 58 (2019), no. 2, Art. 46, 51 pp. (arXiv) (Journal)
    
    
21. Quantitative homogenization in nonlinear elasticity for small loads.
    together with Stefan Neukamm
    Arch. Ration. Mech. Anal. 230 (2018), no. 1, 343-396. (arXiv) (Journal)
    
    
22. On continuum limits of herogeneous discrete systems modelling cracks in composite materials.
    together with Laura Lauerbach and Anja Schlömerkemper
    GAMM-Mitt. 40 (2018), no. 3, 178-200. (Journal)
    
    
23. On Lennard-Jones systems with finite range interactions and their asymptotic analysis.
    together with Anja Schlömerkemper
    Netw. Heterog. Media 13 (2018), no. 1, 95-118. (arXiv) (Journal)
    
    
24. Stochastic homogenization of nonconvex discrete energies with degenerate growth.
    together with Stefan Neukamm and Anja Schlömerkemper
    SIAM J. Math. Anal. 49 (2017), no. 3, 1761-1809. (arXiv) ( Journal)
    
    
25. Plates with Incompatible Prestrain.
    together with Kaushik Bhattacharya and Marta Lewicka
    Arch. Ration. Mech. Anal. 221 (2016), no. 1, 143-181. (arXiv) Journal)
    
    
26. On a Gamma-convergence analysis of a quasicontinuum method.
    together with Anja Schlömerkemper
    Multiscale Model. Simul. 13 (2015), no. 1, 132-172. (arXiv) (Journal)