Abstract

A new proof based on F. Browder’s ideology is given for the theorem on the approximation of weak solutions of the Laplace equation in a bounded domain \(\Omega \subset {{\mathbb{R}}^{n}}\), \(n \geqslant 2\), with a connected Lipschitz boundary by harmonic polynomials in the Lebesgue space \({{L}_{p}}(\Omega )\) and the Sobolev space \(W_{p}^{1}(\Omega )\).

中文翻译：

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用调和多项式逼近拉普拉斯方程的弱解。

摘要

基于F. Browder意识形态的新证明为定理\（\ Omega \ subset {{\ mathbb {R}} ^ {n}} \）中的Laplace方程的弱解的逼近定理给出，\（n \ geqslant 2 \），在Lebesgue空间\（{{L} _ {p}}（\ Omega）\）和Sobolev空间\（W_ {p} ^ { 1}（\ Omega）\）。