Dimension Bounds in Monotonicity Methods for the Helmholtz Equation
Harrach, B., Pohjola, V., & Salo, M. (2019). Dimension Bounds in Monotonicity Methods for the Helmholtz Equation. SIAM Journal on Mathematical Analysis, 51(4), 2995-3019. https://doi.org/10.1137/19M1240708
Published inSIAM Journal on Mathematical Analysis
© 2019 Society for Industrial and Applied Mathematics
The article [B. Harrach, V. Pohjola, and M. Salo, Anal. PDE] 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.
PublisherSociety for Industrial and Applied Mathematics
ISSN Search the Publication Forum0036-1410
Publication in research information system
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Related funder(s)Academy of Finland; European Commission
Funding program(s)Centre of Excellence, AoF; Academy Project, AoF
The content of the publication reflects only the author’s view. The funder is not responsible for any use that may be made of the information it contains.
Additional information about fundingThe work of the third author was supported by the Academy of Finland (Centre of Excellence in Inverse modeling and Imaging) grants 312121, 309963, and by the European Research Council under Horizon 2020 grant ERC CoG 770924
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