GENERALIZATION OF A FIRST ORDER NON-LINEAR COMPLEX ELLIPTIC SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS IN SOBOLEV SPACE

  • MAMOURIAN, A. (Dept. of Mathematics, Faculty of Science, Tehran University) ;
  • TAGHIZADEH, N. (Dept. of Mathematics, Faculty of Science, University of Guilan)
  • Received : 2001.12.26
  • Published : 2002.07.30

Abstract

In this paper we discuss on the existence of general solution of Partial Differential Equations $\frac{{\partial}w}{{\partial}\bar{z}}=F(z,\;w,\;\frac{{\partial}w}{{\partial}z})+G(z,\;w,\;\bar{w})$ in the Sololev Space $W_{1,p}(D)$, that is generalization of a first order Non-linear Elliptic System of Partial Differential Equations $\frac{{\partial}w}{{\partial}\bar{z}}=F(z,\;w,\;\frac{{\partial}w}{{\partial}z}).$

Keywords

partial differential equations;holomorphic function;Banach spaces

References

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