3-调和函数的Dirichlet问题

The Dirichlet Problem for 3-harmonic Function

给出了3-调和函数的Dirichlet问题的一种解法,先通过多调和函数的弱分解定理将其转化为等价的2个独立的3-解析函数的Hilbert边值问题,再转化为等价的几个解析函数的Dirichlet问题来求解,得出了原问题解的存在唯一性定理.

In this paper, a new approach for solving the Dirichlet problem for 3 - harmonic function was given. First, the problem was converted into two independent and equivalent Hilbert boundary value problems for trianalytic functions using the weak decomposition theorem for polyharmonic functions, and then into several e- quivalent Dirichlet boundary value problems for analytic functions.