Related papers: Reconstructions from boundary measurements on admi…

We consider the problem of developing a method to reconstruct a potential $q$ from the partial data Dirichlet-to-Neumann map for the Schr\"odinger equation $(-\Delta_g+q)u=0$ on a fixed admissible manifold $(M,g)$. If the part of the…

We show that a continuous potential $q$ can be constructively determined from the knowledge of the Dirichlet-to-Neumann map for the Schr\"odinger operator $-\Delta_g+q$ on a conformally transversally anisotropic manifold of dimension $\geq…

We prove that a continuous potential $q$ can be constructively determined from the knowledge of the Dirichlet-to-Neumann map for the perturbed biharmonic operator $\Delta_g^2+q$ on a conformally transversally anisotropic Riemannian manifold…

We consider the restricted Dirichlet-to-Neumann map $\Lambda^{U,V}_{g,A,q}$ for the wave equation with magnetic potential $A$ and scalar potential $q$, on an admissible Lorentzian manifold $(M, g)$ of dimension $n \geq 3$ with boundary.…

Let $(\Omega^3,g)$ be a compact smooth Riemannian manifold with smooth boundary and suppose that $U$ is a an open set in $\Omega$ such that $g|_U$ is the Euclidean metric. Let $\Gamma= \overline{U} \cap \partial \Omega$ be connected and…

In this paper we prove two results. The first shows that the Dirichlet-Neumann map of the operator $\Delta_g+q$ on a Riemannian surface can determine its topological, differential, and metric structure. Earlier work of this type assumes a…

Let $(\Omega^3,g)$ be a compact smooth Riemannian manifold with smooth boundary and suppose that $U$ is an open set in $\Omega$ such that $g|_U$ is the Euclidean metric. Let $\Gamma= \overline{U} \cap \partial \Omega$ be non-empty,…

This article gives a complex analysis lighting on the problem which consists in restoring a bordered connected riemaniann surface from its boundary and its Dirichlet-Neumann operator. The three aspects of this problem, unicity,…

For a compact, connected, oriented Riemannian $3$-manifold $(M, g)$ with smooth boundary $\partial M$, we explicitly give a local representation and a full symbol expression for the electromagnetic Dirichlet-to-Neumann map by factorizing…

In a previous article of Dos Santos Ferreira, Kenig, Salo and Uhlmann, anisotropic inverse problems were considered in certain admissible geometries, that is, on compact Riemannian manifolds with boundary which are conformally embedded in a…

We consider the inverse problem of determining a potential in a semilinear elliptic equation from the knowledge of the Dirichlet-to-Neumann map. For bounded Euclidean domains we prove that the potential is uniquely determined by the…

We consider the inverse problem of recovering the magnetic and potential term of a magnetic Schr\"{o}dinger operator on certain compact Riemannian manifolds with boundary from partial Dirichlet and Neumann data on suitable subsets of the…

We consider the Dirichlet-to-Neumann map $\Lambda$ on a cylinder-like Lorentzian manifold related to the wave equation related to the metric $g$, a magnetic field $A$ and a potential $q$. We show that we can recover the jet of $g,A,q$ on…

We consider the problem of reconstructing of the boundary of an unknown inclusion together with its conductivity from the localized Dirichlet-to-Neumann map. We give an exact reconstruction procedure and apply the method to an inverse…

In this paper we show that following Nachman's method we can still reconstruct complex conductivities in $C^{1,1}$ from its Dirichlet-to-Neumann map in three and higher dimensions. For such, we analyze all of the results in Nachman and…

We extend the method of layer potentials to manifolds with boundary and cylindrical ends. To obtain this extension along the classical lines, we have to deal with several technical difficulties due to the non-compactness of the boundary,…

We show that on a simple Riemannian manifold, the electric potential and the solenoidal part of the magnetic potential appearing in the magnetic Schr\"odinger operator can be recovered H\"older stably from the boundary spectral data. This…

We prove that the Dirichlet-to-Neumann map of the linear wave equation determines the topological, differentiable and conformal structure of the underlying Lorentzian manifold, under mild technical assumptions. With more stringent geometric…

An electrical potential U on bordered surface X (in Euclidien three-dimensional space) with isotropic conductivity function sigma>0 satisfies equation d(sigma d^cU)=0, where d^c is real operator associated with complex (conforme) structure…

For a compact Riemannian manifold $(M,g)$ with boundary $\partial M$, the Diri\-chl\-et-to-Neumann operator $\Lambda_g:C^\infty(\partial M)\longrightarrow C^\infty(\partial M)$ is defined by $\Lambda_gf=\left.\frac{\partial…