Geometric rigidity on Sobolev spaces with variable exponent and applications

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Nonlinear elasticity (74B20) Methods involving semicontinuity and convergence; relaxation (49J45)

Cites Work

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A derivation of linearized Griffith energies from nonlinear models
Lebesgue and Sobolev spaces with variable exponents
Linear elasticity obtained from finite elasticity by \(\Gamma \)-convergence under weak coerciveness conditions
Piecewise rigidity
Improved Poincaré inequalities with weights
Linear \(\Gamma \)-limits of multiwell energies in nonlinear elasticity theory
New integral estimates for deformations in terms of their nonlinear strains
On Lavrentiev's phenomenon
An introduction to \(\Gamma\)-convergence
Derivation of the nonlinear bending-torsion theory for inextensible rods by \(\Gamma\)-convergence
Linearized elasticity as \(\Gamma\)-limit of finite elasticity
Derivation of a linearised elasticity model from singularly perturbed multiwell energy functionals
Regularity results for stationary electro-rheological fluids
Rigidity estimate for two incompatible wells
A nonlinear model for inextensible rods as a low energy \(\varGamma\)-limit of three-dimensional nonlinear elasticity
Linearized plasticity is the evolutionary \(\Gamma\)-limit of finite plasticity
Quantitative immersability of Riemann metrics and the infinite hierarchy of prestrained shell models
Weak compactness in variable exponent spaces
Griffith energies as small strain limit of nonlinear models for nonsimple brittle materials
Nonlinear and linearized models in thermoviscoelasticity
Variational linearization of pure traction problems in incompressible elasticity
Korn's second inequality and geometric rigidity with mixed growth conditions
On the derivation of linear elasticity from atomistic models
Two-well rigidity and multidimensional sharp-interface limits for solid-solid phase transitions
Global gradient estimates for the \(p(\cdot)\)-Laplacian
A derivation of linear elastic energies from pair-interaction atomistic systems
Minimizers of the variable exponent, non-uniformly convex Dirichlet energy
A hierarchy of plate models derived from nonlinear elasticity by gamma-convergence
Simple proof of two-well rigidity
On the stability of conformal mappings in multidimensional spaces
Sharp rigidity estimates for incompatible fields as a consequence of the Bourgain Brezis div-curl result
On multiwell Liouville theorems in higher dimension
Geometric rigidity for incompatible fields and an application to strain-gradient plasticity
Multiwell Rigidity in Nonlinear Elasticity
Rotation and strain
A Two Well Liouville Theorem
On Korn's second inequality
Weakly Differentiable Functions
On the Passage from Nonlinear to Linearized Viscoelasticity
A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
From atomistic systems to linearized continuum models for elastic materials with voids
Microscopic Validation of a Variational Model of Epitaxially Strained Crystalline Films
Geometric linearization of theories for incompressible elastic materials and applications
Lower Semicontinuity in SBV for Integrals with Variable Growth
Curl bounds Grad on SO(3)
On Lipschitz truncations of Sobolev functions (with variable exponent) and their selected applications
Rigidity and gamma convergence for solid‐solid phase transitions with SO(2) invariance
Regularity results for a class of functionals with non-standard growth
Integral representation and \(\Gamma\)-convergence for free-discontinuity problems with \(p(\cdot)\)-growth
Regularity of minimizers for free-discontinuity problems with p(·)-growth
Lower semicontinuity and relaxation for free discontinuity functionals with non-standard growth

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