具有两个独立变量的二阶椭圆系统的外部边值泊恩卡雷问题

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED Acta Applicandae Mathematicae Pub Date : 2023-12-21 DOI:10.1007/s10440-023-00629-8

F. Criado-Aldeanueva, N. Odishelidze, J. M. Sanchez, M. Khachidze

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引用次数: 0

摘要

本文提供的大量实例表明，在两个独立变量的情况下，带二阶偏导数的线性微分方程系的均匀椭圆性（满足条件 (3)）并不总是导致在诺特意义上所制定的外部椭圆问题的正常可解性。然而，在某些附加条件下，可以从具有椭圆型偏导数的微分方程系中选择在诺特意义上通常可解的类。本文还表明，对于所谓的分解微分方程系，在外部区域具有椭圆型偏导数的情况下，诺特定理是有效的。

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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Exterior Boundary-Value Poincaré Problem for Elliptic Systems of the Second Order with Two Independent Variables

This paper offers a number of examples showing that in the case of two independent variables the uniform ellipticity of a linear system of differential equations with partial derivatives of the second order, which fulfills condition (3), do not always cause the normal solvability of formulated exterior elliptic problems in the sense of Noether.

Nevertheless, from the system of differential equations with partial derivatives of elliptic type it is possible to choose, under certain additional conditions, classes which are normally solvable in the sense of Noether.

This paper also shows that for the so-called decomposed system of differential equations, with partial derivatives of an elliptic type in the case of exterior regions, the Noether theorems are valid.

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来源期刊

Acta Applicandae Mathematicae 数学-应用数学

CiteScore

2.80

自引率

6.20%

发文量

审稿时长

16.2 months

期刊介绍： Acta Applicandae Mathematicae is devoted to the art and techniques of applying mathematics and the development of new, applicable mathematical methods. Covering a large spectrum from modeling to qualitative analysis and computational methods, Acta Applicandae Mathematicae contains papers on different aspects of the relationship between theory and applications, ranging from descriptive papers on actual applications meeting contemporary mathematical standards to proofs of new and deep theorems in applied mathematics.