The heterogeneous Helmholtz problem with spherical symmetry: Green’s operator and stability estimates

DOI10.3233/ASY-201657MaRDI QIDQ5029343

Céline Torres, Stefan A. Sauter

Publication date: 14 February 2022

Published in: Asymptotic Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.15866

zbMATH Keywords

heterogeneous mediaHelmholtz equationBessel functionsstability estimateshigh frequency

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Stability in context of PDEs (35B35) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Diffraction, scattering (78A45) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Weak solutions to PDEs (35D30) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)

Related Items (2)

Scattering by Finely Layered Obstacles: Frequency-Explicit Bounds and Homogenization ⋮ At the interface between semiclassical analysis and numerical analysis of wave scattering problems. Abstracts from the workshop held September 25 -- October 1, 2022

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Strong unique continuation for general elliptic equations in 2D
• Unique continuation and absence of positive eigenvalues for Schrödinger operators. (With an appendix by E. M. Stein)
• A two-point boundary value problem with a rapidly oscillating solution
• Morrey-Campanato estimates for Helmholtz equations
• Distribution of resonances and local energy decay in the transmission problem. II
• Resonances near the real axis for transparent obstacles
• Stability estimate for the Helmholtz equation with rapidly jumping coefficients
• On the scattered field generated by a ball inhomogeneity of constant index in dimension three
• Convergence analysis for finite element discretizations of the Helmholtz equation with Dirichlet-to-Neumann boundary conditions
• Acoustic transmission problems: Wavenumber-explicit bounds and resonance-free regions
• Stability and finite element error analysis for the Helmholtz equation with variable coefficients
• Asymptotically precise norm estimates of scattering from a small circular inhomogeneity
• Spherical Harmonics in p Dimensions

This page was built for publication: The heterogeneous Helmholtz problem with spherical symmetry: Green’s operator and stability estimates