Convex integration arising in the modelling of shape-memory alloys: some remarks on rigidity, flexibility and some numerical implementations
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Publication:2327832
DOI10.1007/s00332-019-09540-9zbMath1426.35061arXiv1801.08503OpenAlexW2997017875WikidataQ128124922 ScholiaQ128124922MaRDI QIDQ2327832
Angkana Rüland, Christian Zillinger, Jamie M. Taylor
Publication date: 8 October 2019
Published in: Journal of Nonlinear Science (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1801.08503
scaling lawsmaximal regularitysolid-solid phase transformationsconvex integration solutionshigher Sobolev regularitynumerical implementations of convex integration schemes
Smoothness and regularity of solutions to PDEs (35B65) Analytical consequences of geometric convexity (vanishing theorems, etc.) (32F32) Pattern formations in context of PDEs (35B36)
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Cites Work
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- A rigidity result for a reduced model of a cubic-to-orthorhombic phase transition in the geometrically linear theory of elasticity
- The cubic-to-orthorhombic phase transition: rigidity and non-rigidity properties in the linear theory of elasticity
- Comparison of the geometrically nonlinear and linear theories of martensitic transformation
- Asymptotic analysis of hierarchical martensitic microstructure
- Lipschitz-continuous local isometric immersions: rigid maps and origami
- Unexpected solutions of first and second order partial differential equations
- Convexity conditions and existence theorems in nonlinear elasticity
- Implicit partial differential equations
- Parametrized measures and variational principles
- Gagliardo-Nirenberg, composition and products in fractional Sobolev spaces
- Linearized elasticity as \(\Gamma\)-limit of finite elasticity
- A proof of Onsager's conjecture
- The influence of surface energy on stress-free microstructures in shape memory alloys
- Microstructures with finite surface energy: The two-well problem
- The two-well problem in three dimensions
- Convex integration with constraints and applications to phase transitions and partial differential equations
- Sharp commutator estimates via harmonic extensions
- An explicit solution to a system of implicit differential equations
- A variational model allowing both smooth and sharp phase boundaries in solids
- A quantitative rigidity result for the cubic-to-tetragonal phase transition in the geometrically linear theory with interfacial energy
- h-Principle and Rigidity for C 1,α Isometric Embeddings
- Fourier Analysis and Nonlinear Partial Differential Equations
- Onsager's Conjecture for Admissible Weak Solutions
- Some Open Problems in Elasticity
- A rigidity result for a perturbation of the geometrically linear three‐well problem
- Surface energy and microstructure in coherent phase transitions
- Piecewise affine stress-free martensitic inclusions in planar nonlinear elasticity
- Higher Sobolev Regularity of Convex Integration Solutions in Elasticity: The Dirichlet Problem with Affine Data in int(K^{lc})
- A characterisation of the Besov-Lipschitz and Triebel-Lizorkin spaces using Poisson like kernels
- CONVEX INTEGRATION OF DIFFERENTIAL RELATIONS. I
- Nucleation Barriers for the Cubic‐to‐Tetragonal Phase Transformation
- A probabilistic model for interfaces in a martensitic phase transition
- From nonlinear to linearized elasticity via Γ-convergence: The case of multiwell energies satisfying weak coercivity conditions
- Energy scaling and branched microstructures in a model for shape-memory alloys with SO(2) invariance
- An Extension Problem Related to the Fractional Laplacian
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