On vanishing near corners of conductive transmission eigenfunctions
Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
Author(s)
Related Research Unit(s)
Detail(s)
| Original language | English |
|---|---|
| Article number | 2 |
| Journal / Publication | Research in Mathematical Sciences |
| Volume | 9 |
| Issue number | 1 |
| Online published | 7 Dec 2021 |
| Publication status | Published - Mar 2022 |
Link(s)
Abstract
This paper is concerned with the geometric structure of the transmission eigenvalue problem associated with a general conductive transmission condition. We prove that under a mild regularity condition in terms of the Herglotz approximations of one of the pair of the transmission eigenfunctions, the eigenfunctions must be vanishing around a corner on the boundary. The Herglotz approximation is the Fourier extension of the transmission eigenfunction, and the growth rate of the density function can be used to characterize the regularity of the underlying wave function. The geometric structures derived in this paper include the related results in Diao et al. (Commun Partial Differ Equ 46(4):630–679, 2021) and Blåsten and Liu (J Funct Anal 273:3616–3632, 2017) as special cases and verify that the vanishing around corners is a generic local geometric property of the transmission eigenfunctions.
Research Area(s)
- Conductive transmission eigenfunctions, Corner singularity, Geometric structures, Herglotz approximation, Vanishing
Citation Format(s)
On vanishing near corners of conductive transmission eigenfunctions. / Deng, Youjun; Duan, Chaohua; Liu, Hongyu.
In: Research in Mathematical Sciences, Vol. 9, No. 1, 2, 03.2022.Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
