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arXiv · 1901.08495

Dimension bounds in monotonicity methods for the Helmholtz equation

Bastian Harrach·Valter Pohjola·Mikko Salo
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Abstract

The article [HPS] established a monotonicity inequality for the Helmholtz equation and presented applications to shape detection and local uniqueness in inverse boundary problems. The monotonicity inequality states that if two scattering coefficients satisfy $q_1 \leq q_2$, then the corresponding Neumann-to-Dirichlet operators satisfy $\Lambda(q_1) \leq \Lambda(q_2)$ up to a finite dimensional subspace. Here we improve the bounds for the dimension of this space. In particular, if $q_1$ and $q_2$ have the same number of positive Neumann eigenvalues, then the finite dimensional space is trivial.

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Bastian Harrach, Valter Pohjola, Mikko Salo. 2019-01-24. Dimension bounds in monotonicity methods for the Helmholtz equation. https://doi.org/10.1137/19m1240708

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