Approximate Method of Riemann-Hilbert Problem for Elliptic Complex Equations of First Order in Multiply Connected Unbounded Domains

Guochun Wen

LMAM, School of Mathematical Sciences, Peking University, Beijing, China.

DOI: 10.4236/am.2013.41015                

Abstract

In this article, we discuss the approximate method of solving the Riemann-Hilbert boundary value problem for nonlinear uniformly elliptic complex equation of first order

(0.1)

with the boundary conditions

(0.2)

in a multiply connected unbounded domain D, the above boundary value problem will be called Problem A. If the complex Equation (0.1) satisfies the conditions similar to Condition C of (1.1), and the boundary condition (0.2) satisfies the conditions similar to (1.5), then we can obtain approximate solutions of the boundary value problems (0.1) and (0.2). Moreover the error estimates of approximate solutions for the boundary value problem is also given. The boundary value problem possesses many applications in mechanics and physics etc., for instance from (5.114) and (5.115), Chapter VI, [1], we see that Problem A of (0.1) possesses the important application to the shell and elasticity.

Keywords

Approximate Method; Riemann-Hilbert Problem; Nonlinear Elliptic Complex Equations; Multiply Connected Unbounded Domains

Conflicts of Interest

The authors declare no conflicts of interest.

References

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