On positivity sets for Helmholtz solutions
Pu-Zhao Kow, Mikko Salo, Henrik Shahgholian
TL;DR
This paper investigates the existence of Helmholtz solutions that are positive within specified regions, which is relevant for inverse scattering problems involving penetrable obstacles.
Contribution
It demonstrates the existence of solutions positive on the boundary of bounded Lipschitz domains, advancing understanding of Helmholtz solutions in inverse scattering.
Findings
Existence of Helmholtz solutions positive on boundary of Lipschitz domains
Relevance to inverse scattering for penetrable obstacles
Provides constructive insights into positivity sets
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.
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Taxonomy
TopicsNumerical methods in inverse problems · Electromagnetic Scattering and Analysis · Advanced Mathematical Physics Problems