Localized Sensitivity Analysis at High-Curvature Boundary Points of Reconstructing Inclusions in Transmission Problems

@article{Ammari2022LocalizedSA,
  title={Localized Sensitivity Analysis at High-Curvature Boundary Points of Reconstructing Inclusions in Transmission Problems},
  author={Habib M. Ammari and Yat Tin Chow and Hongyu Liu},
  journal={SIAM Journal on Mathematical Analysis},
  year={2022}
}
In this paper, we are concerned with the recovery of the geometric shapes of inhomogeneous inclusions from the associated far field data in electrostatics and acoustic scattering. We present a local resolution analysis and show that the local shape around a boundary point with a high magnitude of mean curvature can be reconstructed more easily and stably. In proving this, we develop a novel mathematical scheme by analyzing the generalized polarisation tensors (GPTs) and the scattering… 
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References

SHOWING 1-10 OF 95 REFERENCES
Weyl's law for the eigenvalues of the Neumann--Poincaré operators in three dimensions: Willmore energy and surface geometry
We deduce eigenvalue asymptotics of the Neumann--Poincar\'e operators in three dimensions. The region $\Omega$ is $C^{2, \alpha}$ ($\alpha>0$) bounded in ${\mathbf R}^3$ and the Neumann--Poincar\'e
A multi-frequency inverse source problem
"J."
however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)
The Foundations Of Differential Geometry
TLDR
The the foundations of differential geometry is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can get it instantly.
Riemannian geometry and geometric analysis
* Established textbook * Continues to lead its readers to some of the hottest topics of contemporary mathematical research This established reference work continues to lead its readers to some of
Spectral approximation for compact operators
In this paper a general spectral approximation theory is developed for compact operators on a Banach space. Results are obtained on the approximation of eigenvalues and generalized eigenvectors.
Characterization of Non-Smooth Pseudodifferential Operators
Smooth pseudodifferential operators on $$\mathbb {R}^{n}$$Rn can be characterized by their mapping properties between $$L^p-$$Lp-Sobolev spaces due to Beals and Ueberberg. In applications such a
Pseudodifferential Operators and Nonlinear PDE
The theory of pseudodifferential operators has played an important role in many investigations into linear PDE. This book is devoted to a summary and reconsideration of some uses of
Quantum ergodicity and localization of plasmon resonances
We are concerned with the geometric properties of the surface plasmon resonance (SPR). SPR is a non-radiative electromagnetic surface wave that propagates in a direction parallel to the negative
Polarization and Moment Tensors: With Applications to Inverse Problems and Effective Medium Theory
Introduction.- Layer Potentials and Transmission Problems.- Uniqueness for Inverse Conductivity Problems.- Generalized Isotropic and Anisotropic Polarization Tensors.- Full Asymptotic Formula for the
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