Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772302 | Journal of Functional Analysis | 2017 | 17 Pages |
Abstract
Let Ω be a bounded domain in Rn, nâ¥2, and VâLâ(Ω) be a potential function. Consider the following transmission eigenvalue problem for nontrivial v,wâL2(Ω) and kâR+,{(Î+k2)v=0inΩ,(Î+k2(1+V))w=0inΩ,wâvâH02(Ω),âvâL2(Ω)=1. We show that the transmission eigenfunctions v and w carry the geometric information of supp(V). Indeed, it is proved that v and w vanish near a corner point on âΩ in a generic situation where the corner possesses an interior angle less than Ï and the potential function V does not vanish at the corner point. This is the first quantitative result concerning the intrinsic property of transmission eigenfunctions and enriches the classical spectral theory for Dirichlet/Neumann Laplacian. We also discuss its implications to inverse scattering theory and invisibility.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Eemeli Blåsten, Hongyu Liu,