最小曲面多项式解的收敛性

IF 0.5 Q3 MATHEMATICS Ufa Mathematical Journal Pub Date : 2016-01-01 DOI:10.13108/2016-8-1-68

A. A. Klyachin, Irina Vladimirovna Truhliaeva

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引用次数: 2

摘要

本文研究了最小曲面方程的Dirichlet问题的多项式近似解。结果表明，在定义域几何结构的一定条件下，解的梯度绝对值随多项式阶的增加而有界。所得性质意味着最小曲面方程的精确解的近似解是一致收敛的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On convergence of polynomial solutions of minimal surface

In this paper we consider the polynomial approximate solutions of the Dirichlet problem for minimal surface equation. It is shown that under certain conditions on the geometric structure of the domain the absolute values of the gradients of the solutions are bounded as the degree of these polynomials increases. The obtained properties imply the uniform convergence of approximate solutions to the exact solution of the minimal surface equation.

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来源期刊

Ufa Mathematical Journal MATHEMATICS-

CiteScore

1.10

自引率

0.00%

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