An improved method for verifying the existence and bounds of the inverse of second-order linear elliptic operators mapping to dual space

被引：5

作者：

Watanabe, Yoshitaka ^{[1
]}

Kinoshita, Takehiko ^{[2
]}

Nakao, Mitsuhiro T. ^{[3
]}

机构：

[1] Kyushu Univ, Res Inst Informat Technol, Nishi Ku, 744 Motooka, Fukuoka, Fukuoka 8190395, Japan

[2] 3-6-18-102 Tomooka,Jyonan Ku, Fukuoka, Fukuoka 8140112, Japan

[3] Waseda Univ, Fac Sci & Engn, Shinjuku Ku, 3-4-1 Okubo, Tokyo 1698555, Japan

来源：

JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS | 2019年 / 36卷 / 02期

关键词：

Solvability of linear problem; Differential operator; Numerical verification; Computer-assisted proof; NUMERICAL VERIFICATION METHOD;

D O I：

10.1007/s13160-019-00344-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper presents an improved method for determining the invertibility of second-order linear elliptic operators with a bound on the norm of their inverses by computers in a mathematically rigorous sense. This approach is an improvement on a previous method (Nakao et al. in Jpn J Ind Appl Math 32:19-32, 2015) which used a projection and constructive a priori error estimates. Several examples confirming the effectiveness of the proposed procedure are reported.

引用

页码：407 / 420

页数：14

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