用压缩、扩展和旋转论证椭圆函数微分方程的 Dirichlet 问题

IF 0.8 Q2 MATHEMATICS

Lobachevskii Journal of Mathematics Pub Date : 2024-08-22 DOI:10.1134/s1995080224601255

L. E. Rossovskii, A. A. Tovsultanov

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引用次数: 0

摘要

摘要本文主要研究在平原有界域中，未知函数的最高导数的压缩（扩展）和旋转参数的线性发散形式二阶函数微分方程的 Dirichlet 问题。以代数形式得到了高定型不等式的必要条件和充分条件。结果可能不仅取决于系数的绝对值，还取决于它们的签名。在对算子结构和域几何的某些限制下，研究了方程中系数和变换参数的所有可能值的广义解的存在性、唯一性和平稳性问题，即使方程不是强椭圆方程。

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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The Dirichlet Problem for an Elliptic Functional Differential Equation with the Compressed, Expanded, and Rotated Argument

Abstract

The paper is devoted to the Dirichlet problem in a plain bounded domain for a linear divergent-form second-order functional differential equation with the compressed (expanded) and rotated argument of the highest derivatives of the unknown function. Necessary and sufficient conditions for the Gårding-type inequality are obtained in algebraic form. The result may depend not only on the absolute value of the coefficients but also on their signature. Under some restrictions on the structure of the operator and the geometry of the domain, the questions of existence, uniqueness, and smoothness of generalized solutions are studied for all possible values of the coefficients and parameters of transformations in the equation, even when the equation is not strongly elliptic.

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来源期刊

Lobachevskii Journal of Mathematics MATHEMATICS-

CiteScore

1.50

自引率

42.90%

发文量

127

期刊介绍： Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.