Uniform approximation by polynomial solutions of second-order elliptic equations, and the corresponding Dirichlet problem

被引：0
作者：
Zaitsev A.B. [1 ]
机构：
[1] Moscow State Institute of Radio Engineering, Electronics, and Automation, Moscow, 119454
来源：
Proceedings of the Steklov Institute of Mathematics | 2006年 / 253卷 / 1期
基金：
俄罗斯基础研究基金会;
关键词：
Dirichlet Problem; STEKLOV Institute; Conformal Mapping; Elliptic Operator; Uniform Approximation;
D O I：
10.1134/S0081543806020064
中图分类号：
学科分类号：
摘要：
Conditions for the uniform approximability of functions by polynomial solutions of second-order elliptic equations with constant complex coefficients on compact sets of special form in ℝ2 are studied. The results obtained are of analytic character. Conditions of solvability and uniqueness for the corresponding Dirichlet problem are also studied. It is proved that the polynomial approximability on the boundary of a domain is not generally equivalent to the solvability of the corresponding Dirichlet problem. © Pleiades Publishing, Inc., 2006.
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页码：57 / 70
页数：13
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