On vanishing near corners of conductive transmission eigenfunctions

This paper is concerned with the geometric structure of transmission eigenvalue problem associated a general conductive condition. We prove that under mild regularity condition in terms Herglotz approximations one pair eigenfunctions, eigenfunctions must be vanishing around corner on boundary. The approximation Fourier extension eigenfunction, and growth rate density function can used to characterize underlying wave function. structures derived this include related results Diao et al. (Commun Partial Differ Equ 46(4):630–679, 2021) Blåsten Liu (J Funct Anal 273:3616–3632, 2017) as special cases verify corners generic local property eigenfunctions.