128 citations · 260 across the 15 of their papers we have counts for
17 papers
Rigidity of Euclidean product structure: breakdown for low Sobolev exponents
Bruce Kleiner, Stefan Müller, László Székelyhidi +1
We develop a general toolbox to study solutions of differential inclusions for unbounded sets . A key notion is the concept that a subset of the s…
Scaling of the elastic energy of small balls for maps between manifolds with different curvature tensors
Milan Krömer, Stefan Müller
Motivated by experiments and formal asymptotic expansions in the physics literature, Maor and Shachar (J. Elasticity 134 (2019), 149-173) studied the behaviour of a model elastic e…
Cauchy-Born Rule from Microscopic Models with Non-convex Potentials
Stefan Adams, Simon Buchholz, Roman Kotecký +1
We study gradient field models on an integer lattice with non-convex interactions. These models emerge in distinct branches of physics and mathematics under various names. In parti…
Optimal order finite difference approximation of generalized solutions to the biharmonic equation in a cube
Stefan Müller, Florian Schweiger, Endre Süli
We prove an optimal order error bound in the discrete norm for finite difference approximations of the first boundary-value problem for the biharmonic equation in spac…
Estimates for the Green's function of the discrete bilaplacian in dimensions 2 and 3
Stefan Müller, Florian Schweiger
We prove estimates for the Green's function of the discrete bilaplacian in squares and cubes in two and three dimensions which are optimal except possibly near the corners of the s…
Data driven problems in elasticity
Sergio Conti, Stefan Müller, Michael Ortiz
We consider a new class of problems in elasticity, referred to as Data-Driven problems, defined on the space of strain-stress field pairs, or phase space. The problem consists of m…
Strict Convexity of the Surface Tension for Non-convex Potentials
Stefan Adams, Roman Kotecký, Stefan Müller
We study gradient models on the lattice with non-convex interactions. These Gibbs fields (lattice models with continuous spin) emerge in various branches of physics…
Energy Bounds for a Compressed Elastic Film on a Substrate
David P. Bourne, Sergio Conti, Stefan Müller
We study pattern formation in a compressed elastic film which delaminates from a substrate. Our key tool is the determination of rigorous upper and lower bounds on the minimum valu…
Folding patterns in partially delaminated thin films
David Bourne, Sergio Conti, Stefan Müller
Michael Ortiz and Gustavo Gioia showed in the 90s that the complex patterns arising in compressed elastic films can be analyzed within the context of the calculus of variations. Th…
Dislocation microstructures and strain-gradient plasticity with one active slip plane
Sergio Conti, Adriana Garroni, Stefan Müller
We study dislocation networks in the plane using the vectorial phase-field model introduced by Ortiz and coworkers, in the limit of small lattice spacing. We show that, in a scalin…
On the optimal constants in Korn's and geometric rigidity estimates, in bounded and unbounded domains, under Neumann boundary conditions
Marta Lewicka, Stefan Muller
We are concerned with the optimal constants: in the Korn inequality under tangential boundary conditions on bounded sets , and in the geometric rigidity esti…
Finite range decomposition for families of gradient Gaussian measures
Stefan Adams, Roman Kotecký, Stefan Müller
Let a family of gradient Gaussian vector fields on be given. We show the existence of a uniform finite range decomposition of the corresponding covariance operator…
Derivation of a rod theory for biphase materials with dislocations at the interface
Stefan Müller, Mariapia Palombaro
Starting from three-dimensional elasticity we derive a rod theory for biphase materials with a prescribed dislocation at the interface. The stored energy density is assumed to be n…
On the commutability of homogenization and linearization in finite elasticity
Stefan Müller, Stefan Neukamm
We study non-convex elastic energy functionals associated to (spatially) periodic, frame indifferent energy densities with a single non-degenerate energy well at SO(n). Under the a…
The time-dependent von Kármán plate equation as a limit of 3d nonlinear elasticity
Helmut Abels, Maria Giovanna Mora, Stefan Müller
The asymptotic behaviour of the solutions of three-dimensional nonlinear elastodynamics in a thin plate is studied, as the thickness of the plate tends to zero. Under appropria…
Large Time Existence for Thin Vibrating Plates
H. Abels, M. G. Mora, S. Müller
We construct strong solutions for a nonlinear wave equation for a thin vibrating plate described by nonlinear elastodynamics. For sufficiently small thickness we obtain existence o…
The uniform Korn - Poincaré inequality in thin domains
Marta Lewicka, Stefan Müller
We study the Korn-Poincaré inequality: \|u\|_{W^{1,2}(S^h)} < C_h \|D(u)\|_{L^2(S^h)}, in domains S^h that are shells of small thickness of order h, around an arbitrary smooth and…