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arXiv · 2301.04965

On positivity sets for Helmholtz solutions

Pu-Zhao Kow·Mikko Salo·Henrik Shahgholian
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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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Pu-Zhao Kow, Mikko Salo, Henrik Shahgholian. 2023-01-12. On positivity sets for Helmholtz solutions. https://doi.org/10.1007/s10013-023-00646-y

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