Asymptotic behavior for the principal eigenvalue of a reinforcement problem

Yachimura, Toshiaki

doi:10.1080/00036811.2018.1517411

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction2

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2020

2022

Publication Types

Select...

Article4

Relationship

Self Cite2

Independent2

Authors

Journals

Cited by 4 publications

(2 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This inverse problem is closely related to the coating problem and reinforcement problem [6,14,7,21,23]. If we consider a two-phase eigenvalue problem with a thin coating of the boundary with Dirichlet boundary condition, then Friedman [14] proved that the principal eigenvalue converges to the principal eigenvalue of a Robin eigenvalue problem.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On an inverse Robin spectral problem

Santacesaria¹,

Yachimura²

2020

Inverse Problems

Self Cite

View full text Add to dashboard Cite

We consider the problem of the recovery of a Robin coefficient on a part γ ⊂ ∂Ω of the boundary of a bounded domain Ω from the principal eigenvalue and the boundary values of the normal derivative of the principal eigenfunction of the Laplace operator with Dirichlet boundary condition on ∂Ω \ γ. We prove uniqueness, as well as local Lipschitz stability of the inverse problem. Moreover, we present an iterative reconstruction algorithm with numerical computations in two dimensions showing the accuracy of the method.

show abstract

Section: Introductionmentioning

confidence: 99%

“…The inverse problem 1.1 is closely related to the coating problem and reinforcement problem [2][3][4][5][6][7]. Let D ⊂ R n (n 2) be a bounded domain with smooth and connected boundary Γ.…”

Section: Introductionmentioning

confidence: 99%