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

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

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 $\frac{{\partial}w}{{\partial}\bar{z}}=F(z,\;w,\;\frac{{\partial}w}{{\partial}z}).$

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