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RESEARCH, PREPRINTS & PUBLICATIONS

RESEARCH INTERESTS

  • Regularity theory for elliptic problems, specifically functionals of linear growth, thereby posed on BV-based spaces (such as BD)

  • Real analysis & function spaces. 

  • L1-estimates and PDEs for measures from a potential theoretic viewpoint, BV^{A}-spaces. 

  • Harmonic Analysis

  • PDEs from mathematical physics, stochastic PDEs.

Find here two exposés explaining and contextualising my research:

COAUTHORS

   Click name to be forwarded to the single webpages:

Selected papers

  • F Gmeineder: The regularity of minima for the Dirichlet problem on BD.                                                                                 (Arch. Ration. Mech. Anal., link to published version). Preprint (Aug 2019, v2, 54 pp.) available here. 

  • F Gmeineder & J Kristensen: Partial regularity for BV minimizers.                                                                                          (Arch. Ration. Mech. Anal., link to published version). Preprint (Mar 2018, 33 pp.) available here.

  • F Gmeineder & J Kristensen: Quasiconvex functionals of $(p,q)$-growth and the partial regularity of relaxed minimizers.   (Arch. Ration. Mech. Anal., link to published version). Preprint (Sep 2022, 90 pp.) available here.

  • F Gmeineder: Partial regularity for symmetric quasiconvex functionals on BD.                                                                        (J. Math. Pures Appl., link to published version) Preprint (Mar 2019, v1, Oct 2019, v2, 40 pp.) available here.

  • D Breit, L Diening & F Gmeineder: On the trace operator for functions of bounded 𝔸-variation.                                    (Analysis & PDE, link to published version). Preprint (Jul 2017, 31 pp.) available here.

  • F Gmeineder, B Raita & J Van Schaftingen: Limiting L¹-estimates on halfspaces.                                                                   (Adv. Math., link to published version). Preprint (Nov 2022, v1, Oct 2023, v2, 20 pp.) available here.

All Preprints & Published Papers

All preprints are available on the ArXiv, too (except for the most recent ones, which usually appear at the ArXiv shortly afterwards). For some of the papers, talk slides are attached for a quick overview.

 

28. The Biot stress - a neo-Hooke-Ciarlet-Geymonat model (...).  w/ D Ghiba, S Holthausen, RJ Martin & P Neff.

      Preprint (Jun 2024, 25 pp.)

27. Divergence-free extensions on L¹-based spaces. w/ S Schiffer

      Preprint (Aug 2024, 50 pp.)

26. Critical KMS inequalities in all dimensions. w/ P Lewintan & J Van Schaftingen

      Preprint (May 2024, 12 pp.) available here.

25. 𝔸-harmonic approximation and partial regularity, revisited. w/ M Bärlin, C Irving & J Kristensen 

      Preprint (Dec 2022, 18 pp.) available here. 

24. Sharp KMS-inequalities for general incompatibilities. w/ P Lewintan & P Neff

      (M³AS - Math. Meth. Mod. Appl. Sc., link to published version), Preprint (Dec 2022, 32 pp.) available here. 

23. Limiting L¹-estimates on halfspaces. w/ B Raita & J Van Schaftingen

      (Adv. Math., link to published version), Preprint (Nov 2022, 22 pp.) available here.

22. Quasiconvex functionals of (p,q)-growth and the partial regularity of relaxed minimizers. w/ J Kristensen

      (Arch. Ration. Mech. Anal., link to published version, Sep 2022, 90 pp.) available here.

21. Optimal incompatible Korn-Maxwell-Sobolev inequalities in all dimensions. w/ P Lewintan & P Neff

      (Calc. Var. PDE, link to published version), Preprint (Jun 2022, 24 pp.) available here.

20. Natural annihilators and operators of constant rank over ℂ. w/ S Schiffer

      (Atti Acc. Rendiconti Lincei (Mat. ed Appl.), link to published version), Preprint (Mar 2022, 18 pp.) available here.

19. On symmetric div-quasiconvex hulls and divsym-free L^∞-truncations. w/ L Behn & S Schiffer

      (Ann. Inst. Henri Poincaré (C), link to published version), Preprint (Aug 2021, 40 pp.) available here.

18. Sharp trace and Korn inequalities for differential operators. w/ L Diening​​

      (Potential Analysis, to appear), Preprint (May 2021, 48 pp.) available here. For an overview talk, click here.

17. On Korn-Maxwell-Sobolev inequalities. w/ D Spector

      (J. Math. Anal. Appl., link to published version). Preprint (Oct 2020, 12 pp.) available here.

16. 𝒜-quasiconvexity and partial regularity. w/ S Conti

      (Calc. Var. PDE, link to published version). Preprint (Sep 2020, 24 pp.) available here.

​15. Riesz potentials for ℂ-elliptic differential operators and continuity points for BV^A maps. w/ L Diening.

      (Q.J. Math. (Oxford), link to published version). Preprint (Nov 2019, 13 pp.) available here.

14. The regularity of minima for the Dirichlet problem on BD.

      (Arch. Ration. Mech. Anal., link to published version). Preprint (Aug 2019, v2, 54 pp.) available here.

13. Partial regularity for symmetric quasiconvex functionals on BD.

      (J. Math. Pures Appl., link to published version) Preprint (Mar 2019, v1, Oct 2019, v2, 40 pp.) available here.

12. The Lipschitz truncation of functions of bounded variation. w/ D Breit & L Diening

      (Indiana Univ. Math. J.). Preprint (Aug 2019, 16 pp.) available here.

11. On limiting trace inequalities for vectorial differential operators. w/ B Raita & J Van Schaftingen

      (Indiana Univ. Math. J.). Preprint (Mar 2019, 30 pp.) available here.

10. Regularity for higher order quasiconvex problems with linear growth from below. w/ J Kristensen

      Preprint (Mar 2019, 5 pp.) available here.

   9. Partial Regularity for BV minimizers. w/ J Kristensen

       (Arch. Ration. Mech. Anal., link to published version). Preprint (Mar 2018) available here. For an overview talk, click here.

   8. Electrorheological fluids under random influences w/ D Breit

       (Stochastics and PDEs: Analysis and Computations, link to published version). Preprint (Mar 2018) available here.

   7. Critical Lp-differentiability of BD-maps. w/ B Raita

       (Rev. Mat. Iberoam., link to published version). Preprint (Feb 2018, title has slightly changed) available here.

   6. On a Neumann problem for functionals with linear growth. w/ M Bulicek & L Beck

       (Annali della Scuola Normale Superiore (Pisa)). Preprint (Jan 2018) available here. For an overview talk, click here.

   5. Limiting embeddings for 𝔸-weakly differentiable functions on domains. w/ B Raita

       (Journal of Functional Analysis (JFA), link to published version) . Preprint (Sep 2017) available here.

   4. On traces for functions of bounded 𝔸-variation. w/ D Breit & L Diening

       (Analysis & PDE, link to published version). Preprint (Jul 2017) available here. For an overview talk, click here.

   3. Sobolev regularity for convex functionals on BD. w/ J Kristensen

       (Calc. Var. PDE, link to published version). Preprint (Mar 2018) available here.

   2. On the singular set of generalised minimisers. 

       (OxPDE technical report 16.03). Preprint (Oct 2016) available here.

   1. Symmetric-convex functionals of linear growth

       (J. Ell. Parab. Equations, 2016). Preprint (Sep 2016) available here.

                                                   

           

In Preparation

​

  • On the convergence of energies principle. /w B Raita & J Kristensen

  • Evolution by minimality for causal variational principles. w/ F Finster

Theses

[T3] Gmeineder, F.: Regularity Theory for Variational Problems on BD. DPhil Thesis, University of Oxford, 2017. xiv+298 pp.                                      Thesis available at ORA.

[T2] Gmeineder, F.: Approximation Theorems for parabolic BV- and BD-spaces, MSc Thesis, University of Munich, 2013. vi +                                      87 pp.

[T1] Gmeineder, F.: Functions of bounded Variation and related Problems in the Calculus of Variations, University of                                                      Munich, 2012. x + 156 pp.

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