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

作　　者：徐婧 黄俊杰[1] 阿拉坦仓 XU Jing;HUANG Junjie;CHEN Alatancang(School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China;School of Mathematical Sciences,Inner Mongolia Normal University Hohhot 010022,China)

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021 [2]内蒙古师范大学数学科学学院,呼和浩特010022

出　　处：《数学年刊（A辑）》2022年第3期227-236,共10页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11961052,No.11761029);内蒙古自治区自然科学基金(No.2021MS01006,No.2020ZD01)的资助。

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{△u=h,在Ω中,-β■u/■v+q△■Ωu-γu=h,在■Ω上的最小范数解,其中Ω■R^(n)是具有光滑边界■Ω的有界域,Δ和Δ■Ω分别是在Ω和■Ω上定义的Laplace(Beltrami)算子,v(x)是在x处的单位外法向量,q,β,γ∈R且q≠0.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,在Ω中,-β■u/■v+q△■Ωu-γu=h,在■Ωwhere Ω■R^(n) is a bounded domain with smooth boundary ■Ω,Δ and Δ■Ω are the corresponding Laplace(Beltrami)operators,v(x)is the unit outer normal at x,and q,β,γ∈R with q≠0.

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 

分 类 号：O177.1[理学—数学]