Estimates of Jacobians by subdeterminants |
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Authors: | Flavia Giannetti Tadeusz Iwaniec Jani Onninen Anna Verde |
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Affiliation: | 1. Dip. di Matematica ed Applicazioni, Universit di Napoli “Federico II,”, 80125, Naples, Italy 2. Department of Mathematics, Syracuse University, 13244, Syracuse, New York 3. Department of Mathematics, University of Jyv?skyl?, P.O. Box 35, Fin-40351, Jyv?skyl?, Finland
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Abstract: | Let ƒ: Ω → ℝn be a mapping in the Sobolev space W1,n−1(Ω,ℝn), n ≥ 2. We assume that the determinant of the differential matrix Dƒ (x) is nonnegative, while the cofactor matrix D#ƒ satisfies , where Lp(Ω) is an Orlicz space. We show that, under the natural Divergence Condition on P, see (1.10), the Jacobian lies in L loc 1 (Ω). Estimates above and below L loc 1 (Ω) are also studied. These results are stronger than the previously known estimates, having assumed integrability conditions on the differential matrix. |
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Keywords: | KeywordHeading" >Math Subject Classifications 42B25 26B10 |
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