Related papers: The Calder\'on problem for quasilinear elliptic eq…

We consider the Calder\`on problem in an infinite cylindrical domain, whose cross section is a bounded domain of the plane. We prove log-log stability in the determination of the isotropic periodic conductivity coefficient from partial…

In this article we focus on inverse problems for a semilinear elliptic equation. We show that a potential $q$ in $L^{n/2+\varepsilon}$, $\varepsilon>0$, can be determined from the full and partial Dirichlet-to-Neumann map. This extends the…

We investigate global uniqueness for an inverse problem for a nonlocal diffusion equation on domains that are bounded in one direction. The coefficients are assumed to be unknown and isotropic on the entire space. We first show that the…

We study a version of Calder\'on's problem for harmonic maps between Riemannian manifolds. By using the higher linearization method, we first show that the Dirichlet-to-Neumann map determines the metric on the domain up to a natural gauge…

This work derives explicit series reversions for the solution of Calder\'on's problem. The governing elliptic partial differential equation is $\nabla\cdot(A\nabla u)=0$ in a bounded Lipschitz domain and with a matrix-valued coefficient.…

In this paper, we consider an inverse problem for a nonlinear wave equation with a damping term and a general nonlinear term. This problem arises in nonlinear acoustic imaging and has applications in medical imaging and other fields. The…

This paper proposes direct and inverse results for the Dirichlet and Dirichlet to Neumann problems for complex curves with nodal type singularities. As an application, we give a method to reconstruct the conformal structure of a compact…

We study an inverse problem for nonlinear elliptic equations modelled after the p-Laplacian. It is proved that the boundary values of a conductivity coefficient are uniquely determined from boundary measurements given by a nonlinear…

A direct reconstruction algorithm based on Calder\'on's linearization method for the reconstruction of isotropic conductivities is proposed for anisotropic conductivities in two-dimensions. To overcome the non-uniqueness of the anisotropic…

The original Calder\'on problem consists in recovering the potential (or the conductivity) from the knowledge of the related Neumann to Dirichlet map (or Dirichlet to Neumann map). Here, we first perturb the medium by injecting small-scaled…

We prove that the knowledge of the Dirichlet-to-Neumann map, measured on a part of the boundary of a bounded domain in $\mathbb{R}^n, n\geq2$, can uniquely determine, in a nonlinear magnetic Schr\"odinger equation, the vector-valued…

We study the inverse problem of determining the coefficients of the fractional power of a general second order elliptic operator given in the exterior of an open subset of the Euclidean space. We show the problem can be reduced into…

In this paper we study the inverse conductivity problem with partial data. Moreover, we show that, in dimension $n\geq 3$ the uniqueness of the Calder\'{o}n problem holds for the $C^{1}\bigcap H^{3/2, 2}$ conductivities.

We detect an inclusion with infinite conductivity from boundary measurements represented by the Dirichlet-to-Neumann map for the conductivity equation. We use both the enclosure method and the probe method. We use the enclosure method to…

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…

In this paper, we address a classical case of the Calder\'on (or conductivity) inverse problem in dimension two. We aim to recover the location and the shape of a single cavity $\omega$ (with boundary $\gamma$) contained in a domain…

The Dirichlet problem and Dirichlet to Neumann map are analyzed for elliptic equations on a large collection of infinite quantum graphs. For a dense set of continuous functions on the graph boundary, the Dirichlet to Neumann map has values…

The Calder\'on problem is an inverse problem with applications to electrical impedance tomography and geophysical prospection. We prove uniqueness in the Calder\'on problem in spatial dimension $n \geq 3$ for scalar conductivities in the…

This short note modifies a reconstruction method by the author (Comm. PDE, 45(9):1118-1133, 2020), for reconstructing piecewise constant conductivities in the Calder\'on problem (electrical impedance tomography). In the former paper, a…

We show that a partial Dirichlet-to-Neumann map, where the measurement set is arbitrarily small, uniquely determines the time-dependent nonlinearity of order three or higher in a semi-linear wave equation up to natural obstructions on a…