On positivity sets for Helmholtz solutions
Analysis of PDEs
2023-09-12 v2
Abstract
We address the question of finding global solutions of the Helmholtz equation that are positive in a given set. This question arises in inverse scattering for penetrable obstacles. In particular, we show that there are solutions that are positive on the boundary of a bounded Lipschitz domain.
Keywords
Cite
@article{arxiv.2301.04965,
title = {On positivity sets for Helmholtz solutions},
author = {Pu-Zhao Kow and Mikko Salo and Henrik Shahgholian},
journal= {arXiv preprint arXiv:2301.04965},
year = {2023}
}
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10 pages