Results 1 
9 of
9
Uniqueness in the Inverse Conductivity Problem for Nonsmooth Conductivities in Two Dimensions
, 1997
"... this paper) imply, via Sobolev embedding, that the conductivity is continuous. It is interesting to note that the only uniqueness results available for conductivities which are discontinuous are due to Kohn and Vogelius [9] who study conductivities which are piecewise analytic and V. Isakov [8] who ..."
Abstract

Cited by 34 (9 self)
 Add to MetaCart
this paper) imply, via Sobolev embedding, that the conductivity is continuous. It is interesting to note that the only uniqueness results available for conductivities which are discontinuous are due to Kohn and Vogelius [9] who study conductivities which are piecewise analytic and V. Isakov [8] who considers a class of conductivities which are piecewise C
Uniqueness in the Inverse Conductivity Problem for Conductivites with 3/2 Derivatives in L^p, p > 2n
"... this paper, we contribute nothing to the analysis of G # . The estimates used are from the paper of Sylvester and Uhlmannn [16]. It is possible that some improvement can be made here. We expect that one should be able to prove uniqueness for conductivities which have 3/2 derivatives in L with p > ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
this paper, we contribute nothing to the analysis of G # . The estimates used are from the paper of Sylvester and Uhlmannn [16]. It is possible that some improvement can be made here. We expect that one should be able to prove uniqueness for conductivities which have 3/2 derivatives in L with p > 2n/3. However, the straightforward generalization of the argument presented below would require that f # #G # f map functions which are compactly supported to functions which are locally in L with p and r satisfying 1/p 1/r = 1/n. Many such estimates fail, see [2] for further discussion
Inverse problems for nonsmooth first order perturbations of the Laplacian
, 2004
"... We consider inverse boundary value problems in Rn, n ≥ 3, for operators which may be written as first order perturbations of the Laplacian. The purpose is to obtain global uniqueness theorems for such problems when the coefficients are nonsmooth. We use complex geometrical optics solutions of Sylves ..."
Abstract

Cited by 8 (4 self)
 Add to MetaCart
We consider inverse boundary value problems in Rn, n ≥ 3, for operators which may be written as first order perturbations of the Laplacian. The purpose is to obtain global uniqueness theorems for such problems when the coefficients are nonsmooth. We use complex geometrical optics solutions of SylvesterUhlmann type to achieve this. A main tool is an extension of the NakamuraUhlmann intertwining method to operators which have continuous coefficients. For the inverse conductivity problem for a C 1+ε conductivity, we construct complex geometrical optics solutions whose properties depend explicitly on ε. This implies the uniqueness result of PäivärintaPanchenkoUhlmann for C 3/2 conductivities. For the magnetic Schrödinger equation, the result is that the DirichlettoNeumann map uniquely determines the magnetic field corresponding to a Dini continuous magnetic potential in C 1,1 domains. For the steady state heat equation with a convection term, we obtain global uniqueness of Lipschitz continuous convection terms in Lipschitz
Calderón inverse problem with partial data on Riemann surfaces
 Duke Math. J
"... Abstract. On a fixed smooth compact Riemann surface with boundary (M0, g), we show that for the Schrödinger operator ∆ + V with potential V ∈ C 1,α (M0) for some α> 0, the DirichlettoNeumann map NΓ measured on an open set Γ ⊂ ∂M0 determines uniquely the potential V. We also discuss briefly the co ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
Abstract. On a fixed smooth compact Riemann surface with boundary (M0, g), we show that for the Schrödinger operator ∆ + V with potential V ∈ C 1,α (M0) for some α> 0, the DirichlettoNeumann map NΓ measured on an open set Γ ⊂ ∂M0 determines uniquely the potential V. We also discuss briefly the corresponding consequences for potential scattering at 0 frequency on Riemann surfaces with asymptotically Euclidean or asymptotically hyperbolic ends. 1.
Identifiability at the boundary for firstorder terms
"... Abstract. Let Ω be a domain in R n whose boundary is C 1 if n ≥ 3 or C 1,β if n = 2. We consider a magnetic Schrödinger operator LW,q in Ω and show how to recover the boundary values of the tangential component of the vector potential W from the Dirichlet to Neumann map for LW,q. We also consider a ..."
Abstract

Cited by 5 (5 self)
 Add to MetaCart
Abstract. Let Ω be a domain in R n whose boundary is C 1 if n ≥ 3 or C 1,β if n = 2. We consider a magnetic Schrödinger operator LW,q in Ω and show how to recover the boundary values of the tangential component of the vector potential W from the Dirichlet to Neumann map for LW,q. We also consider a steady state heat equation with convection term ∆+2W · ∇ and recover the boundary values of the convection term W from the Dirichlet to Neumann map. Our method is constructive and gives a stability result at the boundary. 1
CARLEMAN ESTIMATES AND INVERSE PROBLEMS FOR DIRAC OPERATORS
, 709
"... Abstract. We consider limiting Carleman weights for Dirac operators and prove corresponding Carleman estimates. In particular, we show that limiting Carleman weights for the Laplacian also serve as limiting weights for Dirac operators. As an application we consider the inverse problem of recovering ..."
Abstract

Cited by 4 (4 self)
 Add to MetaCart
Abstract. We consider limiting Carleman weights for Dirac operators and prove corresponding Carleman estimates. In particular, we show that limiting Carleman weights for the Laplacian also serve as limiting weights for Dirac operators. As an application we consider the inverse problem of recovering a Lipschitz continuous magnetic field and electric potential from boundary measurements for the Pauli Dirac operator. 1.
INVERSE BOUNDARY VALUE PROBLEMS FOR THE MAGNETIC SCHRÖDINGER EQUATION
, 2006
"... Abstract. We survey recent results on inverse boundary value problems for the magnetic Schrödinger equation. 1. ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Abstract. We survey recent results on inverse boundary value problems for the magnetic Schrödinger equation. 1.
Uniqueness in the Inverse Conductivity Problem for
"... this paper, we contribute nothing to the analysis of G . The estimates used are from the paper of Sylvester and Uhlmannn [16]. It is possible that some improvement can be made here. We expect that one should be able to prove uniqueness for conductivities which have 3/2 derivatives in L with p > ..."
Abstract
 Add to MetaCart
this paper, we contribute nothing to the analysis of G . The estimates used are from the paper of Sylvester and Uhlmannn [16]. It is possible that some improvement can be made here. We expect that one should be able to prove uniqueness for conductivities which have 3/2 derivatives in L with p > 2n=3. However, the straightforward generalization of the argument presented below would require that f ! rG f map functions which are compactly supported to functions which are locally in L with p and r satisfying 1=p 1=r = 1=n. Many such estimates fail, see [2] for further discussion