# 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)
• Published : 2002.07.30
• 32 2

#### 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

1. Lecture Notes in Math v.798 Reduction of the Problem of Linear conjugation for First order Nonlinear Elliptic Systems in the plane to an Analogous Problem for Holomorphic Function;Analytic Functions Kozubnik 1979 Tutschke, W.;Lawrynowicz, J.(ed.)
2. Generalized Analytic Functions Vekua, I.N.
3. Complex Analysis Methods and Trends and Applications Lanckau, E.;Tutschke, W.
4. Functional Analytic Methods in Complex Analysis and Applications to Partial Differential Equations Seif Mshimba, A.;Tutschke, W.
5. Math Nachr v.99 Construction of the solution to Dirichlet Boundary Value Problem in $W_{1,p}$(D) for Systems of Partial Differential Equations in the plane Seif Mshimba, A.
6. Matem.Sbornik v.31 no.73 Elliptic first order System of Partial Differential Equations Boundary Value Problems Vekua, I.N.