Uniqueness in Calderón's problem for conductivities with unbounded gradient

DOI10.1007/s00220-015-2460-3zbMath1456.35230arXiv1410.2201OpenAlexW3098543326MaRDI QIDQ500062

Boaz Haberman

Publication date: 7 October 2015

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.2201

zbMATH Keywords

inverse conductivity problemuniformly elliptic conductivities in \({W^{s,p}(\Omega)}\)

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Inverse problems for PDEs (35R30) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items

On some partial data Calderón type problems with mixed boundary conditions ⋮ Propagation and recovery of singularities in the inverse conductivity problem ⋮ Inverse problems on low-dimensional manifolds ⋮ The Calderón problem with partial data for conductivities with 3/2 derivatives ⋮ GLOBAL UNIQUENESS FOR THE CALDERÓN PROBLEM WITH LIPSCHITZ CONDUCTIVITIES ⋮ Inverse boundary value problems for polyharmonic operators with non-smooth coefficients ⋮ Global Identifiability of Low Regularity Fluid Parameters in Acoustic Tomography of Moving Fluid ⋮ Uniqueness in inverse acoustic scattering with unbounded gradient across Lipschitz surfaces ⋮ Cloaking for a quasi-linear elliptic partial differential equation ⋮ Determination of singular time-dependent coefficients for wave equations from full and partial data ⋮ Reconstruction of the derivative of the conductivity at the boundary ⋮ The Born approximation in the three-dimensional Calderón problem. II: Numerical reconstruction in the radial case ⋮ On instability mechanisms for inverse problems ⋮ The anisotropic Calderón problem for singular metrics of warped product type: the borderline between uniqueness and invisibility ⋮ The Calderón problem with corrupted data ⋮ Low regularity theory for the inverse fractional conductivity problem ⋮ Identifiability of electrical and heat transfer parameters using coupled boundary measurements ⋮ Characterization for stability in planar conductivities ⋮ SUFFICIENT CONDITIONS FOR THE EXISTENCE OF LIMITING CARLEMAN WEIGHTS ⋮ Calderón's problem for some classes of conductivities in circularly symmetric domains ⋮ A multiscale theory for image registration and nonlinear inverse problems ⋮ Note on Calderón's inverse problem for measurable conductivities ⋮ A bilinear strategy for Calderón's problem ⋮ A nonlinear Plancherel theorem with applications to global well-posedness for the defocusing Davey-Stewartson equation and to the inverse boundary value problem of Calderón ⋮ Probabilistic interpretation of the Calderón problem ⋮ Scattering with critically-singular and \(\delta \)-shell potentials ⋮ Recovery of Nonsmooth Coefficients Appearing in Anisotropic Wave Equations ⋮ Uniqueness in the Calderón problem and bilinear restriction estimates ⋮ ON NONUNIQUENESS FOR THE ANISOTROPIC CALDERÓN PROBLEM WITH PARTIAL DATA ⋮ Partial data inverse problem with 𝐿^{𝑛/2} potentials ⋮ Infinite-dimensional inverse problems with finite measurements ⋮ CALDERÓN’S INVERSE PROBLEM WITH A FINITE NUMBER OF MEASUREMENTS ⋮ Reconstruction and stability for piecewise smooth potentials in the plane ⋮ The Born approximation in the three-dimensional Calderón problem ⋮ A partial data result for less regular conductivities in admissible geometries

Cites Work

• Unnamed Item
• Unnamed Item
• A global uniqueness theorem for an inverse boundary value problem
• A unique continuation theorem for exterior differential forms on Riemannian manifolds
• Limiting Carleman weights and anisotropic inverse problems
• Carleman estimates and inverse problems for Dirac operators
• The trace of Sobolev-Slobodeckij spaces on Lipschitz domains
• Uniform Sobolev inequalities and unique continuation for second order constant coefficient differential operators
• A property of measures in \(\mathbb{R}{}^ N\) and an application to unique continuation
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• On a counterexample concerning unique continuation for elliptic equations in divergence form
• Complex geometrical optics solutions for Lipschitz conductivities.
• On nonuniqueness for Calderón's inverse problem
• Singular solutions of elliptic equations and the determination of conductivity by boundary measurements
• Uniqueness in Calderón's problem with Lipschitz conductivities
• On an inverse boundary value problem
• Uniqueness in an inverse boundary problem for a magnetic Schrödinger operator with a bounded magnetic potential
• The borderlines of invisibility and visibility in Calderón's inverse problem
• Carleman estimates and unique continuation for second-order elliptic equations with nonsmooth coefficients
• Recovering the conductivity at the boundary from the Dirichlet to Neumann map: a pointwise result
• Nonunique continuation for uniformly parabolic and elliptic equations in selfadjoint divergence form with Hölder continuous coefficients
• GLOBAL UNIQUENESS FOR THE CALDERÓN PROBLEM WITH LIPSCHITZ CONDUCTIVITIES
• A Problem in Electrical Prospection and a n-Dimensional Borg-Levinson Theorem
• Determining conductivity by boundary measurements
• Inverse boundary value problems at the boundary—continuous dependence
• Global Uniqueness in the Impedance-Imaging Problem for Less Regular Conductivities
• TheX^s_θspaces and unique continuation for solutions to the semilinear wave equation
• Cloaking via change of variables in electric impedance tomography
• A restriction theorem for the Fourier transform