Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Three Characteristic Beltrami System in Even Dimensions (I): p-Harmonic Equation

  • Gao, Hongya (College of Mathematics and Computer Science, Hebei University) ;
  • Chu, Yuming (Department of Mathematics, Huzhou Normal College) ;
  • Sun, Lanxiang (Department of Mathematics, Cangzhou Teacher's College)
  • Received : 2004.09.20
  • Published : 2007.09.23
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Abstract

This paper deals with space Beltrami system with three characteristic matrices in even dimensions, which can be regarded as a generalization of space Beltrami system with one and two characteristic matrices. It is transformed into a nonhomogeneous $p$-harmonic equation $d^*A(x,df^I)=d^*B(x,Df)$ by using the technique of out differential forms and exterior algebra of matrices. In the process, we only use the uniformly elliptic condition with respect to the characteristic matrices. The Lipschitz type condition, the monotonicity condition and the homogeneous condition of the operator A and the controlled growth condition of the operator B are derived.

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References

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