论椭圆域中适当椭圆方程迪里夏特问题的高效解法

Pub Date : 2024-04-25 DOI:10.3103/s1068362324700018

A. H. Babayan, R. M. Veziryan

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引用次数: 0

摘要

摘要在椭圆域中考虑了具有多根的四阶适当椭圆方程。找到了该方程的 Dirichlet 问题唯一可解性的必要条件和充分条件，并确定了如果这些条件失败，该问题的缺陷数。问题的解以显式形式求得。

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 an Efficient Solution of the Dirichlet Problem for Properly Elliptic Equation in the Elliptic Domain

Abstract

The fourth-order properly elliptic equation with multiple root is considered in the elliptic domain. The conditions, necessary and sufficient for the unique solvability of the Dirichlet problem for this equation are found, and if these conditions fail the defect numbers of this problem are determined. The solution of the problem is found in explicit form.

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