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

Guochun Wen^{*}

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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.

References

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[2] G. C. Wen, “Linear and Nonlinear Elliptic Complex Equations,” Shanghai Scientific and Technical Publishers, Shanghai, 1986.

[3] G. C. Wen and H. Begehr, “Boundary Value Problems for Elliptic Equations and Systems,” Longman Scientific and Technical Company, Harlow, 1990.

[4] G. C. Wen, “Approximate Methods and Numerical Analysis for Elliptic Complex Equations,” Gordon and Breach, Amsterdam, 1999.

[5] G. C. Wen, D. C. Chen and Z. L. Xu, “Nonlinear Complex Analysis and Its Applications,” Mathematics Monograph Series 12, Science Press, Beijing, 2008.

[6] G. C. Wen, “Recent Progress in Theory and Applications of Modern Complex Analysis,” Science Press, Beijing, 2010.