| 徐婧,黄俊杰,阿拉坦仓.一类耦合算子矩阵的极大Tseng 逆及其在椭圆方程中的应用*[J].数学年刊A辑,2022,43(3):227~236 |
| 一类耦合算子矩阵的极大Tseng 逆及其在椭圆方程中的应用* |
| Maximal Tseng Inverse of a Class of Coupled Operator Matrices and its Application to an Elliptic Equation |
| Received:December 21, 2021 Revised:October 06, 2022 |
| DOI：10.16205/j.cnki.cama.2022.0015 |
| 中文关键词: 耦合算子矩阵, 广义逆, 椭圆方程, 动态边界条件, 最小范数解 |
| 英文关键词:Coupled operator matrix, Generalized inverse, Elliptic equation,Dynamical boundary condition, Minimum norm solution |
| 基金项目:国家自然科学基金(No.11961052，No.11761029) 和内蒙古自治区自然科学基金(No.2021MS01006, No.2020ZD01) |
| Author Name | Affiliation | | XU Jing | In this paper, a necessary and sufficient condition is given for a one-sided coupled operator matrix to have the maximal Tseng inverse with Banachiewicz-Schur form. The result is applied to finding the minimum norm solution of the elliptic equation with dynamical boundary condition {?u = h in Ω,? β?u/?ν + q??Ωu ? γu = h on ?Ω,where Ω Rn is a bounded domain with smooth boundary ?Ω, ? and ??Ω are the corresponding Laplace (Beltrami) operators, ν(x) is the unit outer normal at x, and q, β, γ ∈ R with q 6 = 0. | | HUANG Junjie | Corresponding author. School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China. | | CHEN Alatancang | School of Mathematical Sciences, Inner Mongolia Normal University, Hohhot 010022, China. |
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| 中文摘要: |
| 作者给出了单边耦合算子矩阵的极大Tseng逆具有Banachiewicz-Schur形式的充要条件.作为应用, 刻画了具有动态边界条件的椭圆方程{Δu = h 在 Ω 中,-β?u/?ν + qΔ?Ωu -γu = h 在 ?Ω 上,分别是 Ω 的最小范数解, 其中Ω ? Rn是具有光滑边界 ?Ω 的有界域, ? 和 ??Ω 分别是在 Ω 和 ?Ω 上定义的Laplace (Beltrami) 算子, ν(x) 是在 x 处的单位外法向量, q, β, γ ∈ R J q 6 = 0. |
| 英文摘要: |
| In this paper, a necessary and sufficient condition is given for a one-sided coupled operator matrix to have the maximal Tseng inverse with Banachiewicz-Schur form. The result is applied to finding the minimum norm solution of the elliptic equation with dynamical boundary condition {Δu = h in Ω ,-β?u/?ν + qΔ?Ωu -γu = h on ?Ω where Ω Rn is a bounded domain with smooth boundary ?Ω, ? and ??Ω are the corresponding Laplace (Beltrami) operators, ν(x) is the unit outer normal at x, and q, β, γ ∈ R with q 6 = 0. |
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