2019/11/22 by Assia Benabdallah, Benabdallah, Assia, Matania Ben‐Artzi +3
Computer Science · Mathematics · #35P20 I 35Q60 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Optimization and Control (math.OC) #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1911.09947
openalex publication_date 2019/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider the Dirichlet-Laplacian in Ω:= (0,L)× (0,H) and choose another open set ω⊂ Ω. The estimate 0Cω>0,∃ ω, ω\not=∅, such that inf Rω(u)=0,and we wish to characterize these two sets. For two patterns we give a sufficient condition, sometimes necessary. As our operator corresponds to a layered media we can give another representation of its spectrum: i.e. a subset of points of R× R that leads to the suggested partition and others connected results: micro local interpretation, default measures,... Section 4.1 of the previous version was not correct, now it is corrected, many proofs are simplified and a new general result is added.