On Solutions of the Navier Problem for a Polyharmonic Equation in Unbounded Domains

IF 1.7 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL Russian Journal of Mathematical Physics Pub Date : 2023-12-25 DOI:10.1134/s1061920823040209

H.A. Matevossian

引用次数: 0

Abstract

The polyharmonic Navier problem is considered, the uniqueness (non-uniqueness) of its solution is studied in unbounded domains under the assumption that the generalized solution of this problem has a finite Dirichlet integral with weight \(|x|^a\). Depending on the values of the parameter \(a\), uniqueness theorems are proved and exact formulas are found for calculating the dimension of the space of solutions of the Navier problem for a polyharmonic equation in the exterior of a compact set and in a half-space.

DOI 10.1134/S1061920823040209

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论无界域多谐方程的纳维问题解法

摘要考虑了多谐 Navier 问题，在该问题的广义解具有权重 \(|x|^a\) 的有限 Dirichlet 积分的假设下，研究了其解在无界域中的唯一性（非唯一性）。根据参数 \(a\) 的值，证明了唯一性定理，并找到了计算紧凑集外部和半空间中多谐方程的纳维叶问题解的空间维数的精确公式。 doi 10.1134/s1061920823040209

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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来源期刊

Russian Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.