圆柱和半平面域拓扑积的Dirichlet问题

THE DIRICHLET-PROBLEM ON TOPOLOGICAL PRODUCT OF CYLINDRICAL AND HALF-PLANE DOMAINS

在圆柱和上半平面域拓扑积的特征流形上引入一组奇性积分算子M^2,由此来讨论该区域的D irichlet问题和Neum ann问题的解。得到这个区域上的D irichlet边值问题的解的表达式就是它的拓广的Poisson积分表示式。作为它的一个应用,还讨论了这个区域的Neum ann边值问题的解。

This paper established a group of real singular integral operators on characteristic manifold of topological product of cylindrical and haft-plane domains, by which it discussed the solutions of Dirichlet-problem and neumann - problem on this domains. It otained the solution of Dirichlet boundary value problem on this domains is just its extended poisson integral formula. As one of its applications, it also discussed the Neumann boundary value problem.