Related papers: Uniqueness of a Potential from Boundary Data in Lo…

We study a family of non-local isoperimetric energies $E_{\gamma,\varepsilon}$ on the round sphere $M = S^n$, where the non-local interaction kernel $K_\varepsilon$ is the fundamental solution of the Helmholtz operator $1 - \varepsilon^2…

We show that the knowledge of the Dirichlet-to-Neumann map on the boundary of a bounded open set in $\mathbb R^n$, $n\ge 3$, for the perturbed polyharmonic operator $(-\Delta)^m+A\cdot D+q$, $m\ge 2$, with $n>m$, $A\in…

We discuss the inverse problem of determining the, possibly anisotropic, conductivity of a body $\Omega\subset\mathbb{R}^{n}$ when the so-called Neumann-to-Dirichlet map is locally given on a non empty curved portion $\Sigma$ of the…

Let $\Omega =\omega\times\mathbb R$ where $\omega\subset \mathbb R^2$ be a bounded domain, and $V : \Omega \to\mathbb R$ a bounded potential which is $2\pi$-periodic in the variable $x_{3}\in \mathbb R$. We study the inverse problem…

Let $\Delta$ be a building of type $\widetilde A_2$ and order $q$, with maximal boundary $\Omega$. Let $\Gamma$ be a group of type preserving automorphisms of $\Delta$ which acts regularly on the chambers of $\Delta$. Then the crossed…

This work considers the Neumann eigenvalue problem for the weighted Laplacian on a Riemannian manifold $(M,g,\partial M)$ under the singular perturbation. This perturbation involves the imposition of vanishing Dirichlet boundary conditions…

Let $M$ denote a compact, connected Riemannian manifold of dimension $n\in{\mathbb N}$. We assume that $ M$ has a smooth and connected boundary. Denote by $g$ and ${\rm d}v_g$ respectively, the Riemannian metric on $M$ and the associated…

The purpose of this paper is twofold. First, we introduce the notion of a $\Gamma$-martingale on a Euclidean manifold with a boundary (i.e., the closure of an open connected domain in R d ), we provide its equivalent characterization…

This paper deals with the approximation of a magnetic Schr\"odinger operator with a singular $\delta$-potential that is formally given by $(i \nabla + A)^2 + Q + \alpha \delta_\Sigma$ by Schr\"odinger operators with regular potentials in…

This paper addresses the following problem. \begin{equation} \left\{ \begin{array}{lr} -{\Delta}u=\lambda I_\alpha*_\Omega u+|u|^{2^*-2}u\mbox{ in }\Omega ,\nonumber u\in H_0^1(\Omega).\nonumber \end{array} \right. \end{equation} Here,…

We investigate that a potential $V$ in the fractional Schr\"odinger equation $( (-\Delta_g )^s +V ) u=f$ can be recovered locally by using the local source-to-solution map on smooth connected closed Riemannian manifolds. To achieve this…

We study Schr\"{o}dinger operators on star metric graphs with potentials of the form $\alpha\varepsilon^{-2}Q(\varepsilon^{-1}x)$. In dimension 1 such potentials, with additional assumptions on $Q$, approximate in the sense of distributions…

In this paper we prove uniqueness for an inverse boundary value problem for the magnetic Schr\"odinger equation in a half space, with partial data. We prove that the curl of the magnetic potential $A$, when $A\in…

We derive new lower bounds for the first eigenvalue of the Dirac operator of an oriented hypersurface $\Sigma$ bounding a noncompact domain in a spin asymptotically flat manifold (M n , g) with nonnegative scalar curvature. These bounds…

We consider the problem of finding on a given Euclidean domain $\Omega$ of dimension $n \geq 3$ a complete conformally flat metric whose Schouten curvature $A$ satisfies some equation of the form $f(\lambda(-A)) = 1$. This generalizes a…

Let $X$ be a smooth bordered surface in $\real^3$ with smooth boundary and $\hat \sigma$ a smooth anisotropic conductivity on $X$. If the genus of $X$ is given, then starting from the Dirichlet-to-Neumann operator $\Lambda_{\hat \sigma}$ on…

Let $\Omega$ be a bounded domain of $\mathbb{R}^{n+1}$ with $n \ge 1$. We assume that the boundary $\Gamma$ of $\Omega$ is Lipschitz. Consider the Dirichlet-to-Neumann operator $N_0$ associated with a system in divergence form of size $m$…

We consider the inverse problem of recovering a potential from the Dirichlet to Neumann map at a large fixed frequency on certain Riemannian manifolds. We extend the earlier result of [G. Uhlmann and Y. Wang, arXiv:2104.03477] to the case…

Let $G$ be a unimodular Lie group, $X$ a compact manifold with boundary, and $M$ be the total space of a principal bundle $G\to M\to X$ so that $M$ is also a complex manifold satisfying a local subelliptic estimate. In this work, we show…

A generalized variant of the Calder\'on problem from electrical impedance tomography with partial data for anisotropic Lipschitz conductivities is considered in an arbitrary space dimension $n \geq 2$. The following two results are shown:…