Franz Gmeineder

activity

20162026

most citedPartial Regularity for BV Minimizers

34 citations · 172 across the 30 of their papers we have counts for

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33 papers · 1 filter

math.AP2026

The Sharp Ellipticity Threshold for $W^{1, 1}$ -Regularity

Franz Gmeineder

We establish that the ellipticity of the minimal surface integrand is the sharp threshold for $W^{1, 1}$ -regularity of solutions to the Dirichlet problem on $BV$ .…

math.AP2026

Non-uniformly elliptic variational problems on BV

Lisa Beck, Franz Gmeineder, Mathias Schäffner

We establish $W^{1, 1}$ -regularity and higher gradient integrability for relaxed minimizers of convex integral functionals on $BV$ . Unlike classical examples such…

math.AP2025

On the Singular Limit in Hibler's Sea Ice Model

Robert Denk, Franz Gmeineder, Matthias Hieber

We establish the existence of energy-driven solutions to the momentum balance equation in Hibler's sea ice model. As a main novelty and different from previous results, we deal wit…

math.AP2025

Curl Measure Fields, the Generalized Stokes Theorem and Vorticity Fluxes

Gui-Qiang G. Chen, Franz Gmeineder, Monica Torres

We introduce and analyze the class $CM^{p}$ of curl-measure fields that are $p$ -integrable vector fields whose distributional curl is a vector-valued finite Radon measure…

math.AP2025

Rate-form equilibrium for an isotropic Cauchy-elastic formulation: Part I: modeling

Patrizio Neff, Nina J. Husemann, Sebastian Holthausen +2

We derive the rate-form spatial equilibrium system for a nonlinear Cauchy elastic formulation in isotropic finite-strain elasticity. For a given explicit Cauchy stress-strain const…

math.AP2024

Gradient integrability for bounded $BD$ -minimizers

Lisa Beck, Ferdinand Eitler, Franz Gmeineder

We establish that locally bounded relaxed minimizers of degenerate elliptic symmetric gradient functionals on $BD (Ω)$ have weak gradients in $\mathrm{L}_{\mathrm{loc}}^{1}…

math.AP2024

Extensions of divergence-free fields in $L^{1}$ -based function spaces

Franz Gmeineder, Stefan Schiffer

We establish the first extension results for divergence-free (or solenoidal) elements of $L^{1}$ -based function spaces. Here, the key point is to preserve the solenoidalit…

math.AP2024

The Biot stress -- right stretch relation for the compressible Neo-Hooke-Ciarlet-Geymonat model and Rivlin's cube problem

Ionel-Dumitrel Ghiba, Franz Gmeineder, Sebastian Holthausen +2

The aim of the paper is to recall the importance of the study of invertibility and monotonicity of stress-strain relations for investigating the non-uniqueness and bifurcation of h…

math.AP2024

Limiting Korn-Maxwell-Sobolev inequalities for general incompatibilities

Franz Gmeineder, Peter Lewintan, Jean Van Schaftingen

We give sharp conditions for the limiting Korn-Maxwell-Sobolev inequalities \begin{align*} \lVert P\rVert_{\dot{W}{^{k-1,\frac{n}{n-1}}}(\mathbb{R}^n)}\le c\big(\lVert\mathscr{A}[P…

math.AP2022★ 1 cited

$A$ -harmonic approximation and partial regularity, revisited

Matthias Bärlin, Franz Gmeineder, Christopher Irving +1

We give a direct harmonic approximation lemma for local minima of quasiconvex multiple integrals that entails their $C^{1, α}$ or $C^{\infty}$ -partial regularity.…

math.AP2022★ 7 cited

Korn-Maxwell-Sobolev inequalities for general incompatibilities

Franz Gmeineder, Peter Lewintan, Patrizio Neff

We establish a family of coercive Korn-type inequalities for generalised incompatible fields in the superlinear growth regime under sharp criteria. This extends and unifies several…

math.AP2022★ 5 cited

Boundary ellipticity and limiting $L^{1}$ -estimates on halfspaces

Franz Gmeineder, Bogdan Raiţă, Jean Van Schaftingen

We identify necessary and sufficient conditions on $k$ th order differential operators $A$ in terms of a fixed halfspace $H^{+} \subset R^{n}$ such that the Gagliardo--N…

math.AP2022★ 1 cited

Quasiconvex functionals of $(p, q)$ -growth and the partial regularity of relaxed minimizers

Franz Gmeineder, Jan Kristensen

We establish $C^{\infty}$ -partial regularity results for relaxed minimizers of strongly quasiconvex functionals \begin{align*} \mathscr{F}[u;Ω]:=\int_ΩF(\nabla u)\,\mathrm…

math.AP2022★ 19 cited

Optimal incompatible Korn-Maxwell-Sobolev inequalities in all dimensions

Franz Gmeineder, Peter Lewintan, Patrizio Neff

We characterise all linear maps $A : R^{n \times n} \to R^{n \times n}$ such that, for $1 \leq p < n$ , \begin{align*} \|P\|_{L^{p^{*}}(\mathbb{R}^{n})}\leq…

math.AP2022★ 1 cited

Natural annihilators and operators of constant rank over $C$

Franz Gmeineder, Stefan Schiffer

Even if the Fourier symbols of two constant rank differential operators have the same nullspace for each non-trivial phase space variable, the nullspaces of those differential oper…

math.AP2021

On symmetric div-quasiconvex hulls and divsym-free $L^{\infty}$ -truncations

Linus Behn, Franz Gmeineder, Stefan Schiffer

We establish that for any non-empty, compact set $K \subset R_{sym}^{3 \times 3}$ the $1$ - and $\infty$ -symmetric div-quasiconvex hulls $K^{(1)}$ and $K^{(\infty)}$ …

math.AP2021★ 1 cited

Sharp trace and Korn inequalities for differential operators

Lars Diening, Franz Gmeineder

We establish sharp trace- and Korn-type inequalities that involve vectorial differential operators, the focus being on situations where global singular integral estimates are not a…

math.AP2020

On Korn-Maxwell-Sobolev Inequalities

Franz Gmeineder, Daniel Spector

We establish a family of inequalities that allow one to estimate the $L^{q}$ -norm of a matrix-valued field by the $L^{q}$ -norm of an elliptic part and the $\mathr…

math.AP2020

$A$ -Quasiconvexity and Partial Regularity

Sergio Conti, Franz Gmeineder

We establish the first partial regularity result for local minima of strongly $A$ -quasiconvex integrals in the case where the differential operator $A$ possesse…

math.AP2019

Continuity points via Riesz potentials for $C$ -elliptic operators

Lars Diening, Franz Gmeineder

We establish a Riesz potential criterion for Lebesgue continuity points of functions of bounded $A$ -variation, where $A$ is a $C$ -elliptic differential o…

math.AP2019

The Lipschitz truncation of functions of bounded variation

Dominic Breit, Lars Diening, Franz Gmeineder

We construct a Lipschitz truncation which approximates functions of bounded variation in the area-strict metric. The Lipschitz truncation changes the original function only on a sm…

math.AP2019★ 29 cited

On limiting trace inequalities for vectorial differential operators

Franz Gmeineder, Bogdan Raita, Jean Van Schaftingen

We establish that trace inequalities $$\|D^{k-1}u\|_{L^{\frac{n-s}{n-1}}(\mathbb{R}^{n},dμ)} \leq c \|μ\|_{L^{1,n-s}(\mathbb{R}^{n})}^{\frac{n-1}{n-s}}\|\mathbb{A}[D]u\|_{L^{1}(\ma…

math.AP2019★ 1 cited

Regularity for higher order quasiconvex problems with linear growth from below

Franz Gmeineder, Jan Kristensen

We announce new existence and $ε$ -regularity results for minimisers of the relaxation of strongly quasiconvex integrals that on smooth maps $u\colonΩ\subset\mathbb{R}^{n}…

math.AP2019

Partial regularity for symmetric quasiconvex functionals on BD

Franz Gmeineder

We establish the first partial regularity results for (strongly) symmetric quasiconvex functionals of linear growth on BD, the space of functions of bounded deformation. By Rindler…

The Sharp Ellipticity Threshold for W1,1-Regularity

Non-uniformly elliptic variational problems on BV

On the Singular Limit in Hibler's Sea Ice Model

Curl Measure Fields, the Generalized Stokes Theorem and Vorticity Fluxes

Rate-form equilibrium for an isotropic Cauchy-elastic formulation: Part I: modeling

Gradient integrability for bounded BD-minimizers

Extensions of divergence-free fields in L1-based function spaces

The Biot stress -- right stretch relation for the compressible Neo-Hooke-Ciarlet-Geymonat model and Rivlin's cube problem

Limiting Korn-Maxwell-Sobolev inequalities for general incompatibilities

A-harmonic approximation and partial regularity, revisited

Korn-Maxwell-Sobolev inequalities for general incompatibilities

Boundary ellipticity and limiting L1-estimates on halfspaces

Quasiconvex functionals of (p,q)-growth and the partial regularity of relaxed minimizers

Optimal incompatible Korn-Maxwell-Sobolev inequalities in all dimensions

Natural annihilators and operators of constant rank over C

On symmetric div-quasiconvex hulls and divsym-free L∞-truncations

Sharp trace and Korn inequalities for differential operators

On Korn-Maxwell-Sobolev Inequalities

A-Quasiconvexity and Partial Regularity

Continuity points via Riesz potentials for C-elliptic operators

The Lipschitz truncation of functions of bounded variation

On limiting trace inequalities for vectorial differential operators

Regularity for higher order quasiconvex problems with linear growth from below

Partial regularity for symmetric quasiconvex functionals on BD

The Sharp Ellipticity Threshold for $W^{1, 1}$ -Regularity

Gradient integrability for bounded $BD$ -minimizers

Extensions of divergence-free fields in $L^{1}$ -based function spaces

$A$ -harmonic approximation and partial regularity, revisited

Boundary ellipticity and limiting $L^{1}$ -estimates on halfspaces

Quasiconvex functionals of $(p, q)$ -growth and the partial regularity of relaxed minimizers

Natural annihilators and operators of constant rank over $C$

On symmetric div-quasiconvex hulls and divsym-free $L^{\infty}$ -truncations

$A$ -Quasiconvexity and Partial Regularity

Continuity points via Riesz potentials for $C$ -elliptic operators