G. Dolzmann

activity

20092026

most citedOn the theory of relaxation in nonlinear elasticity with constraints on the determinant

40 citations · 96 across the 11 of their papers we have counts for

collaborators

14 papers

math.AP2026

A frame-indifferent rank-one convex function in three dimensions which is not quasiconvex

Sergio Conti, Georg Dolzmann, Patrick Dondl

We construct a function $W : R^{3 \times 3} \to R$ which is frame-indifferent, $W (QF) = W (F)$ for all $Q \in SO (3)$ , rank-one convex, but not quasiconvex. In a nei…

math.AP2026

Uniform $W^{2, m}$ approximation of almost isometric maps

Sergio Conti, Georg Dolzmann, Stefan Müller

This paper shows that an almost-isometric Sobolev map from a Lipschitz subset of an oriented manifold $M$ into another oriented manifold $N$ can be approximated by a map of class $…

math.AP2026

Local Well-Posedness of a Model for Stress-Driven Growth in the Presence of Nutrients

Helmut Abels, Julian Blawid, Georg Dolzmann

A model for morphoelastic growth, that is, growth influenced by elastic stress, driven by the absorption of nutrients is considered. The model features a multiplicative decompositi…

math.AP2025

Regularity Properties of Solutions of a Model for Morphoelastic Growth in the Presence of Nutrients in One Spatial Dimension

Julian Blawid, Georg Dolzmann

Regularity properties of solutions for a class of quasi-stationary models in one spatial dimension for stress-modulated growth in the presence of a nutrient field are proven. At a…

math.AP2024

Optimal rigidity estimates for maps of a compact Riemannian manifold to itself

Sergio Conti, Georg Dolzmann, Stefan Müller

Let $M$ be a smooth, compact, connected, oriented Riemannian manifold, and let $ : M \to R^{d}$ be an isometric embedding. We show that a Sobolev map $f : M \to M$ which…

math.AP2022★ 8 cited

Analytical and numerical relaxation results for models in soil mechanics

Florian Behr, Georg Dolzmann, Klaus Hackl +1

A variational model of pressure-dependent plasticity employing a time-incremental setting is introduced. A novel formulation of the dissipation potential allows one to construct th…

math.AP2022

Stress-modulated growth in the presence of nutrients -- existence and uniqueness in one spatial dimension

Kira Bangert, Georg Dolzmann

Existence and uniqueness of solutions for a class of models for stress-modulated growth is proven in one spatial dimension. The model features the multiplicative decomposition of t…

math.AP2021

Variational models for the interaction of surfactants with curvature -- existence and regularity of minimizers in the case of flexible curves

Christopher Brand, Georg Dolzmann, Alessandra Pluda

Existence and regularity of minimizers for a geometric variational problem is shown. The variational integral models an energy contribution of the interface between two immiscible…

math.AP2014★ 40 cited

On the theory of relaxation in nonlinear elasticity with constraints on the determinant

Sergio Conti, Georg Dolzmann

We consider vectorial variational problems in nonlinear elasticity of the form $I [u] = \int W (D u) d x$ , where $W$ is continuous on matrices with positive determinant and diverges to in…

math.AP2014

Relaxation of a model energy for the cubic to tetragonal phase transformation in two dimensions

Sergio Conti, Georg Dolzmann

We consider a two-dimensional problem in nonlinear elasticity which corresponds to the cubic-to-tetragonal phase transformation. Our model is frame invariant and the energy density…

math.AP2013★ 18 cited

Strong solutions for the Beris-Edwards model for nematic liquid crystals with homogeneous Dirichlet boundary conditions

Helmut Abels, Georg Dolzmann, YuNing Liu

Existence and uniqueness of local strong solution for the Beris--Edwards model for nematic liquid crystals, which couples the Navier-Stokes equations with an evolution equation for…

math.AP2013★ 1 cited

Well-posedness of a fully-coupled Navier-Stokes/Q-tensor system with inhomogeneous boundary data

Helmut Abels, Georg Dolzmann, YuNing Liu

We prove short-time well-posedness and existence of global weak solutions of the Beris--Edwards model for nematic liquid crystals in the case of a bounded domain with inhomogeneous…

math.AP2012★ 26 cited

Korn's second inequality and geometric rigidity with mixed growth conditions

Sergio Conti, Georg Dolzmann, Stefan Müller

Geometric rigidity states that a gradient field which is $L^{p}$ -close to the set of proper rotations is necessarily $L^{p}$ -close to a fixed rotation, and is one key estimate in nonli…

math.AP2009★ 3 cited

The div-curl lemma for sequences whose divergence and curl are compact in W^{-1,1}

Sergio Conti, Georg Dolzmann, Stefan Müller

It is shown that $u_{k} \cdot v_{k}$ converges weakly to $u \cdot v$ if $u_k\weakto u$ weakly in $L^{p}$ and $v_k\weakly v$ weakly in $L^{q}$ with $p, q \in (1, \infty)$ , $1/ p + 1/ q = 1$ , under t…

A frame-indifferent rank-one convex function in three dimensions which is not quasiconvex

Uniform W2,m approximation of almost isometric maps

Local Well-Posedness of a Model for Stress-Driven Growth in the Presence of Nutrients

Regularity Properties of Solutions of a Model for Morphoelastic Growth in the Presence of Nutrients in One Spatial Dimension

Optimal rigidity estimates for maps of a compact Riemannian manifold to itself

Analytical and numerical relaxation results for models in soil mechanics

Stress-modulated growth in the presence of nutrients -- existence and uniqueness in one spatial dimension

Variational models for the interaction of surfactants with curvature -- existence and regularity of minimizers in the case of flexible curves

On the theory of relaxation in nonlinear elasticity with constraints on the determinant

Relaxation of a model energy for the cubic to tetragonal phase transformation in two dimensions

Strong solutions for the Beris-Edwards model for nematic liquid crystals with homogeneous Dirichlet boundary conditions

Well-posedness of a fully-coupled Navier-Stokes/Q-tensor system with inhomogeneous boundary data

Korn's second inequality and geometric rigidity with mixed growth conditions

The div-curl lemma for sequences whose divergence and curl are compact in W^{-1,1}

Uniform $W^{2, m}$ approximation of almost isometric maps