A Proof of Schiffer's Conjecture in Starlike Domain by Far-Field Patterns
Analysis of PDEs
2016-05-18 v2
Abstract
We formulate the Schiffer's conjecture in spectral geometry in the context of scattering theory. The problem is equivalent to finding a non-trivial solution in an interior transmission problem. We compare the back-scattering data of the perturbation along all incident angles. The uniqueness of the inverse scattering problem along each incident direction proves the Schiffer's conjecture.
Keywords
Cite
@article{arxiv.1502.05302,
title = {A Proof of Schiffer's Conjecture in Starlike Domain by Far-Field Patterns},
author = {Lung-Hui Chen},
journal= {arXiv preprint arXiv:1502.05302},
year = {2016}
}