| 1. | Parallel optimal power flow algorithm based on auxiliary problem principle and sequential quadratic programming method
基于辅助问题和序列二次规划法的电网分区并行最优潮流算法 |
| 2. | Secondly , the above priori estimates and the banach - saks theorem provide the existence of h1 weak solution for the auxiliary problems without small parameter e
因此，不难得到辅助问题分别在每个区域上的全局h ~ 1估计。 |
| 3. | In the last , we proof the auxiliary problem has a solution , and by using the fact we suggest one simple algorithm for the variational inequalitiey under some conditions
最后，通过建立了变分不等式的辅助问题存在着解并由此对变分不等式在一定的条件下给出一种更直接的算法。 |
| 4. | Lastly , we will carry out an iteration method , with the help of the interior regularity theorem of elliptic equation , to obtain high order regularity and the corresponding estimates for solutions of the auxiliary problems without small parameter e
然后，重复与周期区域情形相同的方法和论证，可以分别在每个区域上得到其弱解的高阶正则性以及高阶模估计 |
| 5. | The well - posedness and regularity problems of such equations will be dealed with elliptic regularization method . firstly , we construct a family of auxiliary problems with a small parameter e and a large parameter a . the energy estimates will be derivied after some lengthy calculation
具体说，在两区域闭曲线交界附近作辅助问题的解的h ~ 1局部估计，而在每个区域内部的估计可由标准椭圆型方程h ~ 2内估计直接得到。 |
| 6. | Eventually , one may remove the large parameter a from the auxiliary problems by fredholm - riesz - schauder theory and extremal principle . thus the well - posedness and the regularity of the original problem will be obtained in a standard way . for the sake of convenience , we introduce some symbols
最后，利用迹定理和局部化技巧可以把问题在每个区域上的解拼起来，从而得到该类问题在整个一般区域上的hl弱解存在唯一性及解的高阶正则性和高阶模估计 |
