Higher Sobolev regularity of convex integration solutions in elasticity: the planar geometrically linearized hexagonal-to-rhombic phase transformation

DOI10.1007/s10659-018-09719-3zbMath1431.74016OpenAlexW2909790500WikidataQ128571987 ScholiaQ128571987MaRDI QIDQ2303036

Angkana Rüland, Barbara Zwicknagl, Christian Zillinger

Publication date: 28 February 2020

Published in: Journal of Elasticity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10659-018-09719-3

zbMATH Keywords

elasticitydifferential inclusionsolid-solid phase transformationsconvex integration solutionshigher Sobolev regularity

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Micromechanical theories (74A60) Crystals in solids (74N05) Quasiconformal mappings in the complex plane (30C62) Pattern formations in context of PDEs (35B36)

Related Items (8)

On rigidity for the four-well problem arising in the cubic-to-trigonal phase transformation ⋮ 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 ⋮ On the energy scaling behaviour of a singularly perturbed Tartar square ⋮ Rigidity and flexibility in the modelling of shape-memory alloys ⋮ 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

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