6533b85ffe1ef96bd12c10c8
RESEARCH PRODUCT
Dimension bounds in monotonicity methods for the Helmholtz equation
Mikko SaloBastian HarrachValter Pohjolasubject
Helmholtz equationMathematics::Number Theorymontonicity methodMonotonic function01 natural sciencesinversio-ongelmatMathematics::Numerical AnalysisMathematics - Spectral TheoryMathematics - Analysis of PDEsDimension (vector space)FOS: MathematicsHelmholtz equationUniqueness0101 mathematicsSpectral Theory (math.SP)Mathematicsinverse problemsApplied Mathematics010102 general mathematicsMathematical analysisInverse problemMathematics::Spectral Theory010101 applied mathematicsComputational MathematicsNonlinear Sciences::Exactly Solvable and Integrable Systems35R30AnalysisAnalysis of PDEs (math.AP)description
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. peerReviewed
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2019-01-24 |