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Degenerate Weakly (k1, k2)-Quasiregular Mappings

Gao, Hongya;Tian, Dazeng;Sun, Lanxiang;Chu, Yuming

  • Received : 2007.01.12
  • Accepted : 2009.03.10
  • Published : 2011.03.31

Abstract

In this paper, we first give the definition of degenerate weakly ($k_1$, $k_2$-quasiregular mappings by using the technique of exterior power and exterior differential forms, and then, by using Hodge decomposition and Reverse H$\"{o}$lder inequality, we obtain the higher integrability result: for any $q_1$ satisfying 0 < $k_1({n \atop l})^{3/2}n^{l/2}\;{\times}\;2^{n+1}l\;{\times}\;100^{n^2}\;\[2^l(2^{n+3l}+1)\]\;(l-q_1)$ < 1 there exists an integrable exponent $p_1$ = $p_1$(n, l, $k_1$, $k_2$) > l, such that every degenerate weakly ($k_1$, $k_2$)-quasiregular mapping f ${\in}$ $W_{loc}^{1,q_1}$ (${\Omega}$, $R^n$) belongs to $W_{loc}^{1,p_1}$ (${\Omega}$, $R^m$), that is, f is a degenerate ($k_1$, $k_2$)-quasiregular mapping in the usual sense.

Keywords

Degenerate weakly ($k_1$, $k_2$)-quasiregular mapping;exterior power;Hodge decomposition;Reverse H$\"{o}$lder inequality

References

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