Sharp estimates for the Neumann functions and applications to quantitative photo-acoustic imaging in inhomogeneous media

DOI10.1016/j.jde.2012.03.022zbMath1241.31008arXiv1112.2441OpenAlexW2120433046MaRDI QIDQ423592

Habib Ammari, Seick Kim, Hyeonbae Kang

Publication date: 4 June 2012

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1112.2441

zbMATH Keywords

asymptotic expansiondiffusion approximationvariable coefficientsNeumann functionquantitative photo-acoustic imaging

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Boundary value and inverse problems for harmonic functions in higher dimensions (31B20) Green's functions for elliptic equations (35J08)

Related Items (6)

On solving the singular system arisen from Poisson equation with Neumann boundary condition ⋮ An optimal control problem in photoacoustic tomography ⋮ Stability for quantitative photoacoustic tomography revisited ⋮ Singular Value Decomposition of the Wave Forward Operator with Radial Variable Coefficients ⋮ A global stability estimate for the photo-acoustic inverse problem in layered media ⋮ Heat kernel bounds for elliptic partial differential operators in divergence form with Robin-type boundary conditions

Cites Work

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• Global pointwise estimates for Green's matrix of second order elliptic systems
• The Green matrix for strongly elliptic systems of second order with continuous coefficients
• The Green function for uniformly elliptic equations
• Boundary layers on Sobolev-Besov spaces and Poisson's equation for the Laplacian in Lipschitz domains
• Statistical and computational inverse problems.
• Estimates for Green's matrices of elliptic systems by \(L^ p\) theory
• The Green function estimates for strongly elliptic systems of second order
• Photoacoustic Imaging for Attenuating Acoustic Media
• Neumann functions for second order elliptic systems with measurable coefficients
• Mathematical Modeling in Photoacoustic Imaging of Small Absorbers
• Layer potential methods for elliptic homogenization problems
• Reconstruction of the Optical Absorption Coefficient of a Small Absorber from the Absorbed Energy Density
• Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
• L^p bounds on singular integrals in homogenization
• Optical tomography in medical imaging

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