Higher Sobolev regularity of convex integration solutions in elasticity: the planar geometrically linearized hexagonal-to-rhombic phase transformation
In this article we discuss quantitative properties of convex integration solutions arising in problems modeling shape-memory materials. For a two-dimensional, geometrically linearized model case, the hexagonal-to-rhombic phase transformation, we prove the existence of convex integration solutions $u...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article (Journal) |
| Language: | English |
| Published: |
2020
|
| In: |
Journal of elasticity
Year: 2019, Volume: 138, Issue: 1, Pages: 1-76 |
| ISSN: | 1573-2681 |
| DOI: | 10.1007/s10659-018-09719-3 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1007/s10659-018-09719-3
|
| Author Notes: | Angkana Rüland, Christian Zillinger, Barbara Zwicknagl |
| Summary: | In this article we discuss quantitative properties of convex integration solutions arising in problems modeling shape-memory materials. For a two-dimensional, geometrically linearized model case, the hexagonal-to-rhombic phase transformation, we prove the existence of convex integration solutions $u$ with higher Sobolev regularity, i.e., there exists $\theta _{0}>0$ such that $\nabla u \in W^{s,p}_{loc}( \mathbb{R}^{2})\cap L^{\infty }(\mathbb{R}^{2})$ for $s\in (0,1)$, $p\in (1,\infty )$ with $0< sp < \theta _{0}$. We also recall a construction which shows that in very specific situations with additional symmetry much better regularity properties hold. |
|---|---|
| Item Description: | Published: 14 January 2019 Gesehen am 26.05.2021 |
| Physical Description: | Online Resource |
| ISSN: | 1573-2681 |
| DOI: | 10.1007/s10659-018-09719-3 |