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arXiv · 2502.11980

Quasiconvexity and self-improving size estimates

Bogdan Raiţă
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Abstract

We show that M\"uller's $L\log L$ bound $$F(Du)\geq 0,\,Du\in L^p_{\mathrm{loc}}(\mathbb{R}^n)\implies F(Du)\in L\log L_{\mathrm{loc}}(\mathbb{R}^n)$$ for $F =\det$ and $p=n$ holds for quasiconcave $F$ which are homogeneous of degree $p>1$. This contrasts similar Hardy space bounds which hold only for null Lagrangians.

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Bogdan Raiţă. 2025-02-17. Quasiconvexity and self-improving size estimates. https://arxiv.org/abs/2502.11980

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