|
|
| |
| The Generalized Riemann-Hilbert problem For a Multi-connected Region ofSecond Order Non-linear Elliptic Equations |
| |
Citation： |
Li Mingzhong.The Generalized Riemann-Hilbert problem For a Multi-connected Region ofSecond Order Non-linear Elliptic Equations[J].Chinese Annals of Mathematics B,1982,3(5):645~654 |
| Page view： 752
Net amount： 758 |
Authors： |
Li Mingzhong; |
|
|
| Abstract： |
In this paper, we consider the generalized Riemann-Hilbert problem for second order non-linear elliptic complex equation
$\frac{\partial ^2 w}{\partial \bar z ^2}=F(z,w,\frac{\partial w}{\partial \bar z},\frac{\partial w}{\partial z},\frac{\partial ^2 w}{\partial z \partial \bar z}),z\in G$(1)
with the boundary condition
$Re[z^-n_1e^-\pii\alpha_1(z)w]=r_1(z),Re[z^-n_2e^\pi i \alpha_2(z) \frac{\partial w}{\partial \bar z}]=r_2(z),z\in \Gamma$
where $\Gamma=\Gamma_0+\Gamma_1+\cdots+\Gamma_m$ is the smooth boundary of a multi-connected region G,$n_i(i=1,2)$ are called the indices of the boundary value problem.
we also obtain the following existence theorem of generalized solution.
Theorem, suppose that the indices $n_i>m-1$, the coefficients of the complex
equation (1) and the boundary condition (2) satisftes the condition (c),and q^0 is
sufficiently small, then the seneralized Riemann-Hilbert problem.(1), (2)is solvable
and the solution has theexpression (7). |
Keywords： |
|
Classification： |
|
|
|
Download PDF Full-Text
|
|
|
|
