On the nonuniqueness of the solution of a mixed boundary value problem for the Laplace equation

被引：2
|
作者：
Moiseev, T. E. [1 ]
机构：
[1] Moscow MV Lomonosov State Univ, Moscow, Russia
来源：
DIFFERENTIAL EQUATIONS | 2008年 / 44卷 / 05期
基金：
俄罗斯基础研究基金会;
关键词：
Harmonic Function; Integral Representation; Nontrivial Solution; Uniform Convergence; Laplace Equation;
D O I：
10.1134/S0012266108050170
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the solvability of the mixed boundary value problem for the Laplace equation with three distinct boundary conditions, two of which include two directional derivatives with distinct tilt angles and the remaining one is the first boundary condition. An example of a nontrivial solution of the homogeneous problem is given, and conditions under which the problem has a unique solution are established. The solvability of the problem with a nonhomogeneous first boundary condition is studied.
引用
收藏
页码：734 / 736
页数：3
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