Higher Sobolev Regularity of Convex Integration Solutions in Elasticity: The Dirichlet Problem with Affine Data in int(K^{lc})
From MaRDI portal
Publication:4577220
DOI10.1137/17M1149687zbMath1395.35063arXiv1709.02880OpenAlexW2963186818MaRDI QIDQ4577220
Barbara Zwicknagl, Angkana Rüland, Christian Zillinger
Publication date: 17 July 2018
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1709.02880
Smoothness and regularity of solutions to PDEs (35B65) Nonlinear elasticity (74B20) Analysis of microstructure in solids (74N15) Pattern formations in context of PDEs (35B36)
Related Items (13)
Exact constructions in the (non-linear) planar theory of elasticity: from elastic crystals to nematic elastomers ⋮ On rigidity for the four-well problem arising in the cubic-to-trigonal phase transformation ⋮ On the energy scaling behaviour of singular perturbation models with prescribed dirichlet data involving higher order laminates ⋮ A uniqueness criterion and a counterexample to regularity in an incompressible variational problem ⋮ Convex integration solutions for the geometrically nonlinear two-well problem with higher Sobolev regularity ⋮ Higher Sobolev regularity of convex integration solutions in elasticity: the planar geometrically linearized hexagonal-to-rhombic phase transformation ⋮ On the energy scaling behaviour of a singularly perturbed Tartar square ⋮ Rigidity and flexibility in the modelling of shape-memory alloys ⋮ Convex integration arising in the modelling of shape-memory alloys: some remarks on rigidity, flexibility and some numerical implementations ⋮ On a probabilistic model for martensitic avalanches incorporating mechanical compatibility ⋮ The four-state problem and convex integration for linear differential operators ⋮ Energy scaling law for a singularly perturbed four-gradient problem in helimagnetism ⋮ On scaling laws for multi-well nucleation problems without gauge invariances
Cites Work
- Unnamed Item
- Unnamed Item
- The cubic-to-orthorhombic phase transition: rigidity and non-rigidity properties in the linear theory of elasticity
- Asymptotic analysis of hierarchical martensitic microstructure
- Equidimensional isometric maps
- Quasiconvex functions incorporating volumetric constraints are rank-one convex
- Lipschitz-continuous local isometric immersions: rigid maps and origami
- On the \(n\)-dimensional Dirichlet problem for isometric maps
- Fine phase mixtures as minimizers of energy
- Implicit partial differential equations
- Harmonic analysis of the space BV.
- The influence of surface energy on stress-free microstructures in shape memory alloys
- Microstructures with finite surface energy: The two-well problem
- Convex integration with constraints and applications to phase transitions and partial differential equations
- An explicit solution to a system of implicit differential equations
- Single-slip elastoplastic microstructures
- On multiwell Liouville theorems in higher dimension
- A quantitative rigidity result for the cubic-to-tetragonal phase transition in the geometrically linear theory with interfacial energy
- Multiwell Rigidity in Nonlinear Elasticity
- A rigidity result for a perturbation of the geometrically linear three‐well problem
- CONVEX INTEGRATION OF DIFFERENTIAL RELATIONS. I
This page was built for publication: Higher Sobolev Regularity of Convex Integration Solutions in Elasticity: The Dirichlet Problem with Affine Data in int(K^{lc})
