English

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}
}

Comments

10 pages

R2 v1 2026-06-28T08:10:10.584Z