静电场一、四类边值问题的弱问题

The Weak Problems of the First and the Fourth Mixed Boundary Value Problems of the Electrostatic Field in the Sense of Galerkin

本文在Galerkin意义下给出了静电场一、四类混合边值问题的弱问题的等价性,解的唯一性以及广义解连续依赖定解条件(稳定性)的证明,进而证明一、四类混合边值问题的弱问题是适定的。关于第四类非混合边值问题的讨论,待续。

In the sense of Galerkin, this paper gives the proof of the equivalency and the solution uniqueness of the weak problems of the first and the fourth mixed boundary value problems of the electrostatic field. It also proves that the generalized solu- tion should depend continuously on the boundary conditions and that the weak problems are appropriate. As for the fourth non- mixed boundary value problems, they will be delivered later.