Kyungpook Mathematical Journal

  • 제51권1호
  • /
  • Pages.29-36
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  • 2011
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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Some Global Estimates for the Jacobians of Quasiregular Mappings

  • Gao, Hongya (College of Mathematics and Computer Science, Hebei University) ;
  • Ren, Suna (College of Mathematics and Computer Science, Hebei University) ;
  • Sun, Lanxiang (Department of Mathematics, Cangzhou Normal College)
  • 투고 : 2006.05.25
  • 심사 : 2011.01.20
  • 발행 : 2011.03.31
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초록

Some global estimates for the Jacobians of quasiregular mappings f = ($f^1$, $f^2$, ${\cdots}$, $f^n$) of the Sobolev class $W^{1,n}$(${\Omega}$, $R^n$) in $L^{\varphi}({\mu})$-domains and John domains are established.

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참고문헌

  1. G. Bao and S. Ding, Invariance properties of $L^{\varphi}({\mu})$-domains under some mappings, J. Math. Anal. Appl., 259(2001), 241-252. https://doi.org/10.1006/jmaa.2001.7446
  2. S. Ding and C. A. Nolder, $L^{s}({\mu})$-averaging domains, J. Math. Anal. Appl., 283(2003), 85-99. https://doi.org/10.1016/S0022-247X(03)00216-6
  3. F. W. Gehring, The $L^p$-integrability of partial derivatives of a quasiconformal mapping, Acta Math., 130(1973), 265-277. https://doi.org/10.1007/BF02392268
  4. J. Hogan, C. Li, A. McInton and K. Zhang, Global higher integrability of Jacobians on bounded domains, Ann. Inst. H.Poincare Anal., 17(2000), 193-217. https://doi.org/10.1016/S0294-1449(00)00108-6
  5. T. Iwaniec and C. Sbordone, On the integrability of the Jacobian under minimal hypotheses, Arch. Rational Mech. Anal., 119(1992), 129-143. https://doi.org/10.1007/BF00375119
  6. T. Iwaniec and S. Ding, Global estimates for the Jacobians of orientation-preserving mappings, Compu. Math. Appl., 50(2005), 707-718. https://doi.org/10.1016/j.camwa.2005.04.014
  7. T. Iwaniec, G. Martin, Geometric function theory and nonlinear analysis, Clarendon Press, Oxford, 2001.
  8. S. Muller, Higher integrability of determinants and week convergence in $L^1$, J. Reine Angew. Math., 412(1990), 20-34.
  9. C. A. Nolder, Hardy-Littlewood theorems for A-harmonic tensors, Illinois J. Math., 43(1999), 613-631.