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.
Highlights
We prove the uniqueness of solutions of Problem
Where k1, k2 , k3 are non-negative constants as stated in (1.3), (1.6) and (1.10)
Summary
Let D be an N 1 -connected domain including the infinite point with the boundary. Suppose that the complex Equation (1.1) satisfies the following conditions, namely. 3) The complex Equation (1.1) satisfies the uniform ellipticity condition, i.e. for any U1,U2 , the following inequality in almost every point z D holds:. WEN in which q0 1 is a non-negative constant. Problem A: The Riemann-Hilbert boundary value problem for the complex Equation (1.1) may be formulated as follows: Find a continuous solution w z of (1.1) on. In which 0 1 , k0 , k2 are non-negative constants. This boundary value problem for (1.1) with. Problem B1: Find a continuous solution w z of the complex Equation (1.1) in D satisfying the boundary condition. We may assume that the solution w z satisfies the following side conditions (point conditions). We sometimes will subsume the integral conditions or the point conditions under boundary conditions
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