determining conductivity by boundary measurements ii interior results abstract in a recent paper the authors showed that an unknown real analytic conductivity gamma may be determined from static boundary measurements in this document they extend this analysis by demonstrating that a similar result holds for piecewise real analytic conductivities in addition for the special case of a layered structure it is shown that a three times continuously differentiable conductivity is identifiable by boundary measurements originator supplied keywords include inversion convergence algorithms estimates coefficients

an inverse boundary value problem for schrodinger operators with vector potentials we consider the schrodinger operator for a magnetic potential a and an electric potential q which are supported in a bounded domain in r n with n 3 we prove that knowledge of the dirichlet to neumann map associated to the schrodinger operator determines the magnetic field rot a and the electric potential 4 simultaneously provided rot a is small in the l topology

comment on a p calderon s paper on an inverse boundary value problem in seminar on numerical analysis and its applications to continuum physics rio de janeiro 1980 65 73 soc brasil mat rio de janeiro 1980 mr0590275 81k 35160

multidimensional inverse problems and completeness of the products of solutions to pde a method is given for proving uniqueness theorems for some inverse problems the method is based on a result on completeness of the products of solutions to pde as an example the following uniqueness theorems are proved 1 the scattering amplitude a k known for all s2 and a fixed k 0 determines the compactly supported q x l2 d uniquely 2 the surface data u x y k known for all x y p x x3 0 and a fixed k 0 determine the compactly supported x l2 d d r 3 x x3 0 is arbitrarily small determine aj x j 1 2 uniquely here 2u k2u k2a1x a2 x u x y in r3 a1 l2 d a2 h2 d the same conclusion holds if the surface data are known at two distinct frequencies 4 the surface data u x y k known for all x y p and all k 0 determine v x and h k uniquely here 2 k2 k2 x u x y h k x l2 d h k is fourier transform of a wavelet of compact support 5 the conductivity x w2 2 d x c 0 is uniquely determined by the measurements of u and un on d here n is the outward normal to d d r3 is a bounded domain with a smooth boundary d x u 0 in d 6 necessary and sufficient conditions are given for a function a k s2 k 0 is fixed to be the scattering amplitude corresponding to a local potential from a certain class

determining anisotropic real analytic conductivities by boundary measurements if an electrical potential is applied to the surface of a solid body the current flux across the surface depends on the conductivity in the interior of the body we want to consider the inverse problem of determining the conductivity by these boundary measurements

the inverse sturm liouville problem ii soit q q 0 2 l r 2 0 1 le probleme de sturm liouville y q x y y 0 x 1 y 0 cos y 0 sin 0 y 1 cos y 1 sin 0 a un spectre discret de valeurs propres simples 0 q 1 q avec des fonctions propres h 0 x q h 1 x q on fixe p dans 0 2 l r 2 0 1 et soit m p q 0 2 l r 2 0 1 n q n p n 0 l espace de tous les points q de meme spectre que p on etudie m p comme une sous variete de 0 2 l r 2 0 1

a uniqueness theorem for an inverse boundary value problem in electrical prospection we show that a near constant conductivity of a two dimensional body can be uniquely determined by steady state direct current measurements at the boundary mathematically we show that the coefficient in the operator is uniquely determined by its dirichlet integrals

on the uniqueness of inverse problems from incomplete boundary data we present a generalization of our previous results on the uniqueness of inverse coefficient problems for elliptic equations the theorem proved here is formulated for piecewise constant coefficients with piecewise smooth interfaces of discontinuities which require local boundary data we consider problems with coefficients unknown at one side as well as at both sides of the boundary the uniqueness of the former is proven the latter can yield up to two solutions the proofs are based on a simple analysis of singularities of the green functions the presented approach exactly conforms to some important inverse problems arising in applications of electromagnetic geophysics

recovery of singularities for formally determined inverse problems in this paper we considered several formally determined problems in two dimensions there are no global identifiability results for these problems however we can recover an important feature of these functions namely their singularities more precisely we prove that one can determine the location and strength of singularities of anl compactly supported potential by knowing the associated scattering amplitude at a fixed energy also we prove that one can determine the location and strength of the singularities of the sound speed of a medium by making measurements just on the boundary of the medium

probing for electrical inclusions with complex spherical waves let a physical body in 2 or 3 be given assume that the electric conductivity distribution inside consists of conductive inclusions in a known smooth background further assume that a subset is available for boundary measurements it is proved using hyperbolic geometry that certain information about the location of the inclusions can be exactly recovered from static electric measurements on more precisely given a ball b with center outside the convex hull of and satisfying b boundary measurements on with explicitly given dirichlet data are enough to determine whether b intersects the inclusion an approximate detection algorithm is introduced based on the theory numerical experiments in dimension two with simulated noisy data suggest that the algorithm finds the inclusion free domain near and is robust against measurement noise 2007 wiley periodicals inc

discrete approximations and fixed set iterations in banach spaces we study autonomous differential inclusions with right hand sides satisfying a one sided lipschitz osl condition in banach spaces with uniformly convex duals we first show that the solution set is closed and obtain estimates for euler type discrete approximations we then use these results to derive an analogue of the exponential formula for the reachable set as well as results regarding the existence and approximation of a strongly invariant attractor in the case of a negative osl constant as a by product conditions for controllability of the reverse time system are obtained

determining conductivity by boundary measurements a p calderon pose la question est il possible de determiner la conductivite thermique d un objet a partir de mesures statiques de la temperature et du flux de chaleur a la limite on demontre que ces mesures determinent de facon unique la conductivite thermique et toutes ses derivees a la limite

uniqueness for formally determined inverse boundary value problems abstract in this paper we study the inverse conductivity problem in two dimensions this problem is reduced to a formally determined inverse boundary value problem for the schrodinger equation some recent generic uniqueness results for the inverse problems will be discussed and a new continuous dependence result presented

on the construction of a potential from cauchy data abstract we investigate the problem of recovering a potential q y in the differential equation u q y u 0 x y 0 1 0 1 u 0 y u 1 y u x 0 0 u x 1 f x u y x 1 g x the method of separation of variables reduces the recovery of q y to a nonstandard inverse sturm liouville problem an asymptotic formula is developed that suggests that under appropriate conditions on the cauchy pair f g q y is uniquely determined up to the mean moreover the recovery of q y is comparable to finding a function from its polynomial moments a reconstruction scheme is suggested and numerical examples are considered

a multiscale theory for image registration and nonlinear inverse problems abstract in an influential paper tadmor et al 2004 42 introduced a hierarchical decomposition of an image as a sum of constituents of different scales here we construct analogous hierarchical expansions for diffeomorphisms in the context of image registration with the sum replaced by composition of maps we treat this as a special case of a general framework for multiscale decompositions applicable to a wide range of imaging and nonlinear inverse problems as a paradigmatic example of the latter we consider the calderon inverse conductivity problem we prove that we can simultaneously perform a numerical reconstruction and a multiscale decomposition of the unknown conductivity driven by the inverse problem itself we provide novel convergence proofs which work in the general abstract settings yet are sharp enough to prove that the hierarchical decomposition of tadmor nezzar and vese converges for arbitrary functions in l 2 a problem left open in their paper we also give counterexamples that show the optimality of our general results

inverse problems for metal oxide semiconductor field effect transistor contact resistivity inverse problems arising from the identification of transistor contact resistivity and contact window location are studied a one point boundary measurement of the potential is shown to be sufficient to identify each from a one parameter monotone family and such identification is both stable and continuously dependent on the parameter for a nonmonotone family of locations with resistivity given similar results are obtained for measurement made on almost all boundary points

the calderon problem with partial data in two dimensions we prove for a two dimensional bounded domain that the cauchy data for the schrodinger equation measured on an arbitrary open subset of the boundary determines uniquely the potential this implies for the conductivity equation that if we measure the current fluxes at the boundary on an arbitrary open subset of the boundary produced by voltage potentials supported in the same subset we can determine uniquely the conductivity we use carleman estimates with degenerate weight functions to construct appropriate complex geometrical optics solutions to prove the results

on uniqueness in the general inverse transmisson problem in this paper we demonstrate uniqueness of a transparent obstacle of coefficients of rather general boundary transmission condition and of a potential coefficient inside obstacle from partial dirichlet to neumann map or from complete scattering data at fixed frequency the proposed transmission problem includes in particular the isotropic elliptic equation with discontinuous conductivity coefficient uniqueness results are shown to be optimal hence the considered form can be viewed as a canonical form of isotropic elliptic transmission problems proofs use singular solutions of elliptic equations and complex geometrical optics determining an obstacle and boundary conditions i e reflecting and transmitting properties of its boundary and interior is of interest for acoustical and electromagnetic inverse scattering for modeling fluid structure interaction and for defects detection

identification problems in linear elasticity let be a bounded domain inrnwithc2 boundary and letdbe a lipschitz domain withd we consider the inverse problem determiningd to the system of linear elasticitydi d ij rs ir js d ir js djus 0in where d d rn dand d d rn d under the condition on the lame constants 0 we show thatdis uniquely determined by the complete knowledge of the dirichlet to neumann map we also obtain an uniqueness result for the monotone case from one boundary measurement

consistent approximations for optimal control problems based on runge kutta integration this paper explores the use of runge kutta integration methods in the construction of families of finite dimensional consistent approximations to nonsmooth control and state constrained optimal control problems consistency is defined in terms of epiconvergence of the approximating problems and hypoconvergence of their optimality functions a significant consequence of this concept of consistency is that stationary points and global solutions of the approximating discrete time optimal control problems can only converge to stationary points and global solutions of the original optimal control problem the construction of consistent approximations requires the introduction of appropriate finite dimensional subspaces of the space of controls and the extension of the standard runge kutta methods to piecewise continuous functions it is shown that in solving discrete time optimal control problems that result from runge kutta integration a non euclidean inner product and norm must be used on the control space to avoid potentially serious ill conditioning effects

an inverse problem for the plate in the love kirchhoff theory this paper studies an inverse boundary value problem for the equation of the flexure of the linear inhomogeneous isotropic thin plate in the context of the love kirchhoff theory it is shown that the young modulus e and the poisson ratio nu of the material forming the plate can be determined by the dirichlet to neumann map the boundary values of e nu and their finitely many derivatives if e and nu are close enough to constants in a suitable sense

direct reconstructions of conductivities from boundary measurements the problem of reconstructing an unknown electric conductivity from boundary measurements has applications in medical imaging geophysics and nondestructive testing a nachman ann of math 2 143 1996 pp 71 96 proved global uniqueness for the two dimensional inverse conductivity problem using a constructive method of proof based on this proof siltanen mueller and isaacson inverse problems 16 2000 pp 681 699 presented a new numerical reconstruction method that solves the nonlinear problem directly without iteration the method was verified with nonnoisy rotationally symmetric examples in this paper the method is extended by introducing a new regularization scheme which is analyzed theoretically and tested on symmetric and nonsymmetric numerical examples containing computer simulated noise

comment on calderon s paper on an inverse boundary value problem calder6n determined a method to approximate the conductivity a of a con ducting body in rn for n 2 based on measurements of boundary data the approximation is good in the l norm provided that the conductivity is a small perturbation from a constant we calculate the approximation exactly for the case of homogeneous concentric conducting disks in r2 with different conductivities here the difference in the conductivities is the perturbation we show that the approximation yields precise information about the spatial variation of a even when the perturbation is large this ability to distinguish spatial regions with different conductivities is important for clinical monitoring applications

global uniqueness for a two dimensional inverse boundary value problem we show that the coefficient y x of the elliptic equation vie qyvu 0 in a two dimensional domain is uniquely determined by the corresponding dirichlet to neumann map on the boundary and give a reconstruction pro

singular solutions of elliptic equations and the determination of conductivity by boundary measurements abstract we improve some results on uniqueness and stability in the determination of the coefficient a in the equation i div a grad u 0 in when all possible pairs of dirichlet and neumann data on are known we also treat cases of anisotropic equations our method relies on the construction of solutions to i having an isolated singularity with prescribed asymptotic behaviour

finding conductivity from surface measurements abstract a method is given to determine conductivity of a body from the measurements of the potential and either normal component of the current on the surface of the body or the normal derivative of the potential on and the value of conductivity at a single point on

a uniqueness theorem for an inverse boundary value problem in two dimensions abstract we consider the inverse problem to determine the potential q entering the schrodinger equation u qu 0 in a bounded smooth domain in r 2 in terms of the boundary measurements dirichlet to neumann map when n 3 the uniqueness for the inverse problem was well established in this paper we prove the uniqueness in two dimensions under the assumption that the lp p 2 norm of q is small this result improves a uniqueness result of sylvester uhlmann under the assumption that the w1 norm of q is small

on the continuum limit of a discrete inverse spectral problem on optimal finite difference grids we consider finite difference approximations of solutions of inverse stur m liouville problems in bounded intervals using three point finite difference sc hemes we discretize the equations on so called optimal grids constructed as follow s for a staggered grid with 2k points we ask that the finite difference operator a k k jacobi matrix and the sturm liouville differential operator share the k lowest eigenvalues and the values of the orthonormal eigenfunctions at one end of the interval this requirement determines uniquely the entries in the jacobi matrix which are grid cell averages of the coefficients in the continuum problem if these coefficients are known we can find the grid which we call optimal becau se it gives by design a finite difference operator with a prescribed spectr al measure we focus attention on the inverse problem where neither the coefficients n or the grid are known a key question in inversion is how to parametrize the coefficients i e how to choose the grid it is clear that to be successful this grid must be close to the optimal one which is unknown fortunately as we show here the grid dependence on the unknown coefficients is weak so the inversion can be done on a pr ecomputed grid for an a priori guess of the unknown coefficients this obse rvation leads to a simple yet efficient inversion algorithm which gives coefficien ts that converge pointwise to the true solution as the number k of data points tends to infinity the cornerstone of our convergence proof is showing that op timal grids provide an implicit natural regularization of the inverse problem by givin g reconstructions with uniformly bounded total variation the analysis is based on a novel explicit perturbation analysis of lanczos recursions and on a discrete