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• W3100294470 abstract "Inspired by Morrey’s Problem (on rank-one convex functionals) and the Burkholder integrals (of his martingale theory) we find that the Burkholder functionals $text {B}_p$, $p geqslant 2$, are quasiconcave, when tested on deformations of the identity $fin mathrm {Id} + {mathscr C}^infty _circ (Omega )$ with $text {B}_p (Df(x)) geqslant 0$ pointwise, or equivalently, deformations such that $|D f |^2 leqslant frac {p}{p-2}J_f$. In particular, quasiconcavity holds in explicit neighbourhoods of the identity map. Among the many immediate consequences, this gives the strongest possible $mathscr L^p$-estimates for the gradient of a principal solution to the Beltrami equation $f_{bar {z}}=mu (z) f_z$, for any $p$ in the critical interval $2leqslant p leqslant 1+1/|mu |_infty$." @default.
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• W3100294470 date "2012-05-01" @default.
• W3100294470 modified "2023-10-17" @default.
• W3100294470 title "Burkholder integrals, Morrey’s problem and quasiconformal mappings" @default.
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• W3100294470 doi "https://doi.org/10.1090/s0894-0347-2011-00718-2" @default.
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