Inverse Problem for a Planar Conductivity Inclusion
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Publication:6113272
DOI10.1137/22m1522395zbMath1521.30022arXiv2206.05593OpenAlexW4379651008MaRDI QIDQ6113272
Johan Helsing, Mikyoung Lim, Doosung Choi, Sangwoo Kang
Publication date: 8 August 2023
Published in: SIAM Journal on Imaging Sciences (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2206.05593
Boundary value problems for second-order elliptic equations (35J25) General theory of conformal mappings (30C35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)
Cites Work
- Solving integral equations on piecewise smooth boundaries using the RCIP method: a tutorial
- Mathematical and statistical methods for multistatic imaging
- Target identification using dictionary matching of generalized polarization tensors
- A global uniqueness theorem for an inverse boundary value problem
- Multidimensional inverse spectral problem for the equation \(-\Delta \psi -(v(x)-Eu(x))\psi =0\)
- Analytical shape recovery of a conductivity inclusion based on Faber polynomials
- Polarization and moment tensors. With applications to inverse problems and effective medium theory
- Corner singularities for elliptic problems: Integral equations, graded meshes, quadrature, and compressed inverse preconditioning
- Faber series method for plane problems of an arbitrarily shaped inclusion
- Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains
- Complex geometrical optics solutions for Lipschitz conductivities.
- Faber series method for two-dimensional problems of an arbitrarily shaped inclusion in piezoelectric materials
- Singular solutions of elliptic equations and the determination of conductivity by boundary measurements
- Global uniqueness for a two-dimensional inverse boundary value problem
- Solving Fredholm second-kind integral equations with singular right-hand sides on non-smooth boundaries
- Identification of an algebraic domain in two dimensions from a finite number of its generalized polarization tensors
- Classification of spectra of the Neumann-Poincaré operator on planar domains with corners by resonance
- Generalized polarization tensors for shape description
- Harmonic interpolation in Fejer points with the Faber polynomials as a basis
- Determination of the unknown coefficient \(k(u)\) in the equation \(\nabla\cdot k(u)\nabla u = 0\) from overspecified boundary data
- Quasiconformal reflections
- Geometric multipole expansion and its application to semi-neutral inclusions of general shape
- Tracking of a Mobile Target Using Generalized Polarization Tensors
- The generalized polarization tensors for resolved imaging. Part I: Shape reconstruction of a conductivity inclusion
- Reconstruction of Less Regular Conductivities in the Plane
- GLOBAL UNIQUENESS FOR THE CALDERÓN PROBLEM WITH LIPSCHITZ CONDUCTIVITIES
- Conductivity interface problems. Part I: Small perturbations of an interface
- An effectivization of the global reconstruction in the Gel'fand-Calderon inverse problem in three dimensions
- Electrical impedance tomography and Calderón's problem
- Computation of Faber Series With Application to Numerical Polynomial Approximation in the Complex Plane
- Determining conductivity by boundary measurements
- Determining conductivity by boundary measurements II. Interior results
- A Faber Series Approach to Cardinal Interpolation
- On a Regularity Theorem for Weak Solutions to Transmission Problems with Internal Lipschitz Boundaries
- On the Uniqueness of Inverse Problems from Incomplete Boundary Data
- Uniqueness in the inverse conductivity problem for nonsmooth conductivities in two dimensions
- The Calderón problem for conormal potentials I: Global uniqueness and reconstruction
- Properties of the Generalized Polarization Tensors
- Conformal Mapping via a Density Correspondence for the Double-Layer Potential
- Corner Effects on the Perturbation of an Electric Potential
- A mathematical and numerical framework for near-field optics
- Construction of GPT-Vanishing Structures Using Shape Derivative
- Electrical impedance tomography
- Geometric series expansion of the Neumann–Poincaré operator: Application to composite materials
- Reconstruction of Domains with Algebraic Boundaries from Generalized Polarization Tensors
- A decay estimate for the eigenvalues of the Neumann-Poincaré operator using the Grunsky coefficients
- Construction of conformal mappings by generalized polarization tensors
- Solutions of the Dirichlet Problem in the Plane by Approximation with Faber Polynomials
- Isoperimetric Inequalities in Mathematical Physics. (AM-27)
- Series Expansions of the Layer Potential Operators Using the Faber Polynomials and Their Applications to the Transmission Problem
- Multi-scale Classification for Electrosensing
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
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