相关论文: The Dirichlet-to-Neumann map for Lorentzian Calder…

In this article, we study the Calder\'on problem for nonlocal generalizations of the semilinear Moore--Gibson--Thompson (MGT) equation and the Jordan--Moore--Gibson--Thompson (JMGT) equation of Westervelt-type. These partial differential…

We study the wave equation on a bounded domain of $\mathbb R^m$ and on a compact Riemannian manifold $M$ with boundary. We assume that the coefficients of the wave equation are unknown but that we are given the hyperbolic…

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 show in two dimensions that measuring Dirichlet data for the conductivity equation on an open subset of the boundary and, roughly speaking, Neumann data in slightly larger set than the complement uniquely determines the conductivity on a…

We consider the unique recovery of a non compactly supported and non periodic perturbation of a Schr\"odinger operator in an unbounded cylindrical domain, also called waveguide, from boundary measurements. More precisely, we prove recovery…

We prove a sharp regularity threshold for uniqueness in two anisotropic Calder\'on-type inverse problems in dimension $n\ge 3$. The main setting is the Riemannian Schr\"odinger problem with fixed scalar potential: for a prescribed…

In this paper, we solve the fractional anisotropic Calder\'on problem with external data in the Euclidean space, in dimensions two and higher, for smooth Riemannian metrics that agree with the Euclidean metric outside a compact set.…

Consider a real-analytic orientable connected complete Riemannian manifold $M$ with boundary of dimension $n\ge 2$ and let $k$ be an integer $1\le k\le n$. In the case when $M$ is compact of dimension $n\ge 3$, we show that the manifold and…

Let $(M,g)$ and $(M',g')$ be non-orientable Riemannian surfaces with fixed boundary $\Gamma$ and fixed Euler characterictic $m$, and $\Lambda$ and $\Lambda'$ be their Dirichlet-to-Neumann maps, respectively. We prove that the closeness of…

The problem of identifying the set of Dirichlet-to-Neumann (DtN) maps arising from conductivities on a smooth domain, among operators acting on functions on the boundary, is a challenging issue in the mathematical analysis of the Calder\'on…

Given $(M,g)$, a compact connected Riemannian manifold of dimension $d \geq 2$, with boundary $\partial M$, we study the inverse boundary value problem of determining a time-dependent potential $q$, appearing in the wave equation…

We consider the Calder\'on problem in the case of partial Dirichlet-to-Neumann map for the system of elliptic equations in a bounded two dimensional domain. The main result of the manuscript is as follows: If two systems of elliptic…

In this paper, we give some simple counterexamples to uniqueness for the Calderon problem on Riemannian manifolds with boundary when the Dirichlet and Neumann data are measured on disjoint sets of the boundary. We provide counterexamples in…

We consider divergence form elliptic equations $Lu:=\nabla\cdot(A\nabla u)=0$ in the half space $\mathbb{R}^{n+1}_+ :=\{(x,t)\in \mathbb{R}^n\times(0,\infty)\}$, whose coefficient matrix $A$ is complex elliptic, bounded and measurable. In…

The magnetic Dirichlet-to-Neumann map encodes the voltage-to-current measurements under the influence of a magnetic field. In the case of surfaces, we provide precise spectral asymptotics expansion (up to arbitrary polynomial power) for the…

For $D$ a bounded domain in $\mathbb R^d, d \ge 2,$ with smooth boundary $\partial D$, the non-linear inverse problem of recovering the unknown conductivity $\gamma$ determining solutions $u=u_{\gamma, f}$ of the partial differential…

The unique determination of a measurable conductivity from the Dirichlet-to-Neumann map of the equation $\mathrm{div} (\sigma \nabla u) = 0$ is the subject of this note. A new strategy, based on Clifford algebras and a higher dimensional…

In this paper we define a Dirichlet-to-Neumann map for a twisted Dirac Laplacian acting on bundle-valued spinors over a spin manifold. We show that this map is a pseudodifferential operator of order 1 whose symbol determines the Taylor…

In this work we establish log-type stability estimates for the inverse potential and conductivity problems with partial Dirichlet-to-Neumann map, where the Dirichlet data is homogeneous on the inaccessible part. This result, to some extent,…

In this paper we establish commmutator estimates for the Dirichlet-to-Neumann Map associated to a divergence form elliptic operator in the upper half-space $\mathbb{R}^{n+1}_+:=\{(x,t)\in \mathbb{R}^n \times (0,\infty)\}$, with uniformly…