Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (4): 953-958.

• Articles • Previous Articles     Next Articles

On Generalized Beltrami System

 GAO Hong-Ya1,2, ZHAO Li-Fang1   

  1. 1.College of Mathematics and Computer Science, Hebei University, Hebei Baoding 071002;
    2.Mathematical Study Center of Hebei Province, Shijiazhuang 050016
  • Received:2008-08-10 Revised:2009-06-02 Online:2010-07-25 Published:2010-07-25
  • Supported by:

    国家自然科学基金(10971224)和河北省自然科学基金数学研究专项(07M003)资助

Abstract:

This paper deals with the generalized Beltrami system
Dtf(x)H(x)Df(x)=J(x, f)2/nG(x).                                              (*)
A homogeneous elliptic equation of divergence type
Div A(x, Df(x))=0
is derived from (*) under the uniformly elliptic conditions on the matrices H(x), G(x) ∈S(n) by using the energy and variational methods. The weak monotonicity properties for the component functions of (*) and a Caccioppoli inequality are also derived.

Key words: Beltrami system, Elliptic equation of divergence type, Energy functional, Weak monotonicity, Caccioppoli inequality

CLC Number: 

  • 30C65
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