Convergence rate of Dirichlet Laplacians on domains with holes to the Schrödinger operator with L^p potential

2023/12/14 by Hiroto Ishida, Ishida, Hiroto
Computer Science · Mathematics · #35B27 (Primary) #47A10 (Secondary) #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2312.08620

openalex publication_date 2023/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the Dirichlet Laplacian A_ε=-Δ in the domain Ω∖\bigcup_i K_iε⊂ℝⁿ with holes K_iε and the Schrödinger operator A=-Δ+V in Ω where V is the Lⁿ(Ω) limit of the density of the capacities cap(K_iε). Strong resolvent convergence for many V∈ W^-1,∞(Ω) was studied by the author. In this paper, we study about convergence rate for A_ε\toA in norm resolvent sense. The case for which V is a constant is studied by Andrii Khrabustovskyi and Olaf Post.

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