Rank-one convex non-quasiconvex integrands are explicitly constructed in R^{2x4}, R^{4x4}_sym, and R^{3x3}_sym, via restrictions and transpositions of Grabovsky's example and a modification of Sverak's example.
A solution to Morrey's problem in $\mathbb{R}^{2\times m}$
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abstract
We construct homogeneous rank-one convex integrands $F\colon \mathbb{R}^{2\times m} \to \mathbb R$ that are nowhere quasiconvex when $m$ is large.
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2026 1verdicts
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Morrey's problem in $\mathbb{R}^{2 \times 4}$ and $\mathbb{R}^{3 \times 3}_\mathrm{sym}$
Rank-one convex non-quasiconvex integrands are explicitly constructed in R^{2x4}, R^{4x4}_sym, and R^{3x3}_sym, via restrictions and transpositions of Grabovsky's example and a modification of Sverak's example.