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- W1569842283 abstract "We give new proof of the theorem of K. Zhang [Z] on biting convergence of Jacobian determinants for mappings of Sobolev class ${mathscr W}^{1,n}(Omega,mathbb{R}^n)$. The novelty of our approach is in using ${mathscr W}^{1,p}$-estimates with the exponents $1leqslant p lt n$, as developed in [IS1], [IL], [I1]. These rather strong estimates compensate for the lack of equi-integrability. The remaining arguments are fairly elementary. In particular, we are able to dispense with both the Chacon biting lemma and the Dunford-Pettis criterion for weak convergence in ${mathscr L}^1(Omega)$. We extend the result to the so-called Grand Sobolev setting. Biting convergence of Jacobians for mappings whose cofactor matrices are bounded in ${mathscr L}^{frac n{n-1}}(mathbb{R}^n)$ is also obtained. Possible generalizations to the wedge products of differential forms are discussed." @default.
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- W1569842283 date "2003-07-01" @default.
- W1569842283 modified "2023-09-25" @default.
- W1569842283 title "Another approach to biting convergence of Jacobians" @default.
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- W1569842283 doi "https://doi.org/10.1215/ijm/1258138195" @default.
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