University of Oulu

Harrach, Bastian; Pohjola, Valter; Salo, Mikko, Dimension bounds in monotonicity methods for the Helmholtz equation, SIAM J. Math. Anal., 51(4), 2995–3019.

Dimension bounds in monotonicity methods for the Helmholtz equation

Saved in:
Author: Harrach, Bastian1; Pohjola, Valter2; Salo, Mikko3
Organizations: 1Institute for Mathematics, Goethe-University Frankfurt, Frankfurt am Main, Germany
2Research Unit of Mathematical Sciences, University of Oulu, Oulu, Finland
3Department of Mathematics and Statistics, University of Jyväskylä, Jyväskylä, Finland
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 0.5 MB)
Persistent link:
Language: English
Published: Society for Industrial and Applied Mathematics, 2019
Publish Date: 2019-09-26


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 q₁ ≤ q₂, then the corresponding Neumann-to-Dirichlet operators satisfy Λ(q₁) ≤ Λ(q₂) up to a finite-dimensional subspace. Here we improve the bounds for the dimension of this space. In particular, if q₁ and q₂ have the same number of positive Neumann eigenvalues, then the finite-dimensional space is trivial.

see all

Series: SIAM journal on mathematical analysis
ISSN: 0036-1410
ISSN-E: 1095-7154
ISSN-L: 0036-1410
Volume: 51
Issue: 4
Pages: 2995 - 3019
DOI: 10.1137/19M1240708
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Copyright information: © 2019, Society for Industrial and Applied Mathematics.