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| The Generalized Riemann^Haseman Problem |
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Citation： |
Yuan Yirang.The Generalized Riemann^Haseman Problem[J].Chinese Annals of Mathematics B,1982,3(6):733~744 |
| Page view： 897
Net amount： 823 |
Authors： |
Yuan Yirang; |
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| Abstract： |
In this paper we study the generalized Riemann—Haseman problem which was given by Vekua, I. N.
Problem (R-H). Find a sectionally generalized holomorphic function w(z) = {w^+(z), w^-(z)} such that
$\frac {\partial w}{\partial \bar z}+B(z)\bar w=0,z\in E$
Here $B(z)\in C_\alpha ^n-1(D^++L),B(z)\in C_\alpha ^n-1(D^- +L),L\in C_\alpha ^n-1,0<\alpha \leq 1,|B(z)|\leq \frac {K}{|z|^1+s}(z\rightarrow \infty),K>0,\varepsilon >0;w(z)$ Satisfies the boundary condition
$\sum\limits_{k=0}^n {a_k(t)\frac {\partial ^k w^+}{\partial t^k}|b_k \frac{\bar \partial ^kw^+}{\partial t^k}}_{t=\alpha(z)}-\sum\limits_{k=0}^n{c_k(t)\frac{\partial ^k w^-}{\partial t^k}+d_k(t)\frac{\bar \partial ^kw^-}{\partial t^k}}=f(t),t\in L$,
Where a_k(t)、 b_k (t) 、 c_k (t) 、d_k(t)、f(t)\in H;\alpha(t) is a mapping of L into itself, $\alpha'(t)\ne 0$and \alpha [\alpha(t)] \equal t.
We study the conditions of the solubility and the number of linearly independent solutions. |
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