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Three Characteristic Beltrami System in Even Dimensions (Ⅰ) : -Harmonic Equation

Gao Hongya|Sun Lanxiang|Chu Yuming
경북대학교 자연과학대학 수학과|2007.09|Kyungpook Mathematical Journal|제47권 제3호|pp. 311-322

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주제분류수학

초록

Abstract

This paper deals with space Beltrami system with three characteristic ma-trices in even dimensions, which can be regarded as a generalization of space Beltramisystem with one and two characteristic matrices. It is transformed into a nonhomoge-neous p-harmonic equation dA(x,dfI ) = dB(x,Df) by using the technique of outerdierential forms and exterior algebra of matrices. In the process, we only use the uni-formly elliptic condition with respect to the characteristic matrices. The Lipschitz typecondition, the monotonicity condition and the homogeneous condition of the operatorAand the controlled growth condition of the operatorB are derived.

참고문헌 (9)

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  3. "Ann. of Math.", pp.586~624 (1992)
  4. "On Beltrami system with two characteristic matrices", 4(22), pp.433~440 (2002)
  5. "Generalized Beltrami system in even dimensions and Beltrami system in high dimensions", 18A(6), pp.789~798 (1997)
  6. "(G,H)-quasiregular mappings and B-harmonic equation", 42(5), pp.883~888 (1999)
  7. "Two characteristic Beltrami equation and quasiregular mappings", 40(5), pp.745~750 (1997)
  8. "Geometric function theory and nonlinear analysis" (2000), Claredon Press
  9. "Analytic foundations of the theory of quasiconformal mappings in Rn", pp.257~324 (1983)

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