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NONLINEAR PDE & CALCULUS OF VARIATIONS

All preprints are available on the ArXiv too. For some of the papers, talk slides are attached for a quick overview.

  • On Hibler's sea ice model in the singular limit. w/ R Denk & M Hieber 

      Preprint (Nov 2025, 54 pp.) available here. 

  • Curl-measure fields, the generalized Stokes theorem and vorticity fluxes. w/ G-Q Chen & M Torres

       Preprint (Sep 2025, 78 pp.) available here.

  • Action-Driven Flows for Causal Variational Principles. w/ F Finster 

        Preprint (Mar 2024, 27 pp.) available here.

  • Rate-Form Equilibrium for an Isotropic Cauchy-Elastic Formulation. Part I: Modeling. w/ Th. Blesgen, S. Holthausen,    N. Husemann & P Neff

       (J. Nonlinear Science, link to published version), Preprint (Apr 2025, 32 pp.) available here

  • On a Nitsche method for incompressible fluids with dynamic boundary conditions. w/ P Gazca, E Maringová & T         

      Tscherpel

      Preprint (Feb 2025, 58 pp.) available here.

  • Gradient integrability for bounded BD-minimizers. w/ L Beck & F Eitler

      (Arch. Ration. Mech. Anal., to appear), Preprint (Dec 2024, 32 pp.) available here.

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

      (U Parma Rev Mat), Preprint (Dec 2022, 18 pp.) available here

  • 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.

  • 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.

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

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

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

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

  • 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.

  • 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.

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

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

  • 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.

  • Electrorheological fluids under random influences w/ D Breit

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

  • 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.

  •  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.

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

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

  • On the singular set of generalised minimisers. 

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

  • Symmetric-convex functionals of linear growth

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

 

Contact Details: 

F Gmeineder

Professorship 'Theory of PDEs'                                                                                 

FB Mathematik & Statistik

Universitätsstraße 10                                 E-Mail: franz.gmeineder (at) uni-konstanz.de

78464 Konstanz, Germany

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