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arXiv · 2608.06367

Quasiconvexity for the Dacorogna--Marcellini Energy

Giuseppe Bruno·Federico Pasqualotto
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Abstract

We prove that the planar Dacorogna--Marcellini energy $f_\gamma(A)=|A|^4-2\gamma|A|^2\det A$ is quasiconvex exactly when it is rank-one convex, i.e. if and only if $|\gamma|\leq\frac{2}{\sqrt3}$. The proof uses a monotonicity property of the energy functional along the componentwise heat flow. As a corollary of our method, we show that for homogeneous quartic polynomials on $2 \times 2$ matrices invariant by left and right rotation, quasiconvexity is equivalent to rank one convexity.

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Giuseppe Bruno, Federico Pasqualotto. 2026-08-06. Quasiconvexity for the Dacorogna--Marcellini Energy. https://arxiv.org/abs/2608.06367

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