Estimates of Jacobians by subdeterminants

Flavia Giannetti, Tadeusz Iwaniec, Jani Kristian Onninen, Anna Verde

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Abstract

Let F: Ω → ℝ n be a mapping in the Sobolev space W 1,n-1(Ω,ℝ n), n > 2. We assume that the determinant of the differential matrix DF (x) is nonnegative, while the cofactor matrix D #F satisfies |D #f|n/n 1 ε L P(ω), where L p(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.

Original languageEnglish (US)
Pages (from-to)223-254
Number of pages32
JournalJournal of Geometric Analysis
Volume12
Issue number2
DOIs
StatePublished - 2002

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Keywords

  • cofactor matrix
  • distributional Jacobian
  • integrability of Jacobian
  • Orlicz space

ASJC Scopus subject areas

  • Mathematics(all)
  • Geometry and Topology

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