Two-by-two upper triangular matrices and Morrey’s conjecture

Terence L.J. Harris; Bernd Kirchheim; Chun Chi Lin

doi:10.1007/s00526-018-1360-8

Two-by-two upper triangular matrices and Morrey’s conjecture

Terence L.J. Harris^*
, Bernd Kirchheim
, Chun Chi Lin

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

It is shown that every homogeneous gradient Young measure supported on matrices of the form (a1,1⋯a1,n-1a1,n0⋯0a2,n) is a laminate. This is used to prove the same result on the 3-dimensional nonlinear submanifold of M^{2 × 2} defined by det X= 0 and X₁₂> 0.

Original language	English
Article number	73
Journal	Calculus of Variations and Partial Differential Equations
Volume	57
Issue number	3
DOIs	https://doi.org/10.1007/s00526-018-1360-8
Publication status	Published - 2018 Jun 1

Keywords

49J45

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1007/s00526-018-1360-8

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title = "Two-by-two upper triangular matrices and Morrey{\textquoteright}s conjecture",

abstract = "It is shown that every homogeneous gradient Young measure supported on matrices of the form (a1,1⋯a1,n-1a1,n0⋯0a2,n) is a laminate. This is used to prove the same result on the 3-dimensional nonlinear submanifold of M2 × 2 defined by det X= 0 and X12> 0.",

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AU - Kirchheim, Bernd

AU - Lin, Chun Chi

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N2 - It is shown that every homogeneous gradient Young measure supported on matrices of the form (a1,1⋯a1,n-1a1,n0⋯0a2,n) is a laminate. This is used to prove the same result on the 3-dimensional nonlinear submanifold of M2 × 2 defined by det X= 0 and X12> 0.

AB - It is shown that every homogeneous gradient Young measure supported on matrices of the form (a1,1⋯a1,n-1a1,n0⋯0a2,n) is a laminate. This is used to prove the same result on the 3-dimensional nonlinear submanifold of M2 × 2 defined by det X= 0 and X12> 0.

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UR - https://www.scopus.com/pages/publications/85045966228#tab=citedBy

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DO - 10.1007/s00526-018-1360-8

M3 - Article

AN - SCOPUS:85045966228

SN - 0944-2669

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JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

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ER -

Two-by-two upper triangular matrices and Morrey’s conjecture

Abstract

Keywords

ASJC Scopus subject areas

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