Related papers: The Dirichlet-to-Neumann Map for Poincar\'e-Einste…

We investigate the continuity of boundary operators, such as the Neumann-to-Dirichlet map, with respect to the coefficient matrices of the underlying elliptic equations. We show that for nonsmooth coefficients the correct notion of…

In this note, we construct a Dirichlet-to-Neumann map, from a Besov space of functions, to the dual of this class. The Besov spaces are of functions on the boundary of a bounded, locally compact uniform domain equipped with a doubling…

In this paper, the elastic Dirichlet-to-Neumann map $\Xi_g$ is studied for the stationary elasticity system in a compact Riemannian manifold $(\Omega,g)$ with smooth boundary $\partial \Omega$. By overcoming methodological difficulties, we…

Boundary conforming coordinates are commonly used in plasma physics to describe the geometry of toroidal domains, for example, in three-dimensional magnetohydrodynamic equilibrium solvers. The magnetohydrodynamic equilibrium configuration…

We construct anisotropic conductivities with the same Dirichlet-to-Neumann map as a homogeneous isotropic conductivity. These conductivities are singular close to a surface inside the body.

In this paper, we study the Dirichlet problem for $p$-convex hypersurfaces with prescribed curvature. We prove that there exists a graphic hypersurface satisfying the prescribed curvature equation with homogeneous boundary condition. An…

In Electrical Impedance Tomography (EIT) one wants to image the conductivity distribution of a body from current and voltage measurements carried out on its boundary. In this paper we consider the underlying mathematical model, the inverse…

We prove a global uniqueness result for the Calder\'{o}n inverse problem for a general quasilinear isotropic conductivity equation on a bounded open set with smooth boundary in dimension $n\ge 3$. Performing higher order linearizations of…

The monotonicity-based approach has become one of the fundamental methods for reconstructing inclusions in the inverse problem of electrical impedance tomography. Thus far the method has not been proven to be able to handle extreme…

We introduce pointwise map smoothness via the Dirichlet energy into the functional map pipeline, and propose an algorithm for optimizing it efficiently, which leads to high-quality results in challenging settings. Specifically, we first…

We use the method of equivariant moving frames to revisit the problem of normal forms and equivalence of nondegenerate real hypersurfaces M \subset C^2 under the pseudo-group action of holomorphic transformations. The moving frame…

In this paper, we first introduce higher order Dirichlet-to-Neumann maps on graphs which can be viewed as a discrete analogue of the corresponding Dirichlet-to-Neumann maps on compact Riemannian manifolds with boundary and a higher order…

We consider a linearized inverse boundary value problem for the elasticity system. From the linearized Dirichlet-to-Neumann map at zero frequency, we show that a transversely isotropic perturbation of a homogeneous isotropic elastic tensor…

The computation of the Dirichlet-Neumann operator for the Laplace equation is the primary challenge for the numerical simulation of the ideal fluid equations. The techniques used commonly for 2D fluids, such as conformal mapping and…

We are concerned with fully nonlinear elliptic equations on complex manifolds and search for technical tools to overcome difficulties in deriving a priori estimates which arise due to the nontrivial torsion and curvature, as well as the…

In this paper we study an integral invariant which obstructs the existence on a compact complex manifold of a volume form with the determinant of its Ricci form proportional to itself, in particular obstructs the existence of a…

We introduce a correspondence between dimer models (and hence superconformal quivers) and the quantum Teichmuller space of the Riemann surfaces associated to them by mirror symmetry. Via the untwisting map, every brane tiling gives rise to…

We derive an integral inequality between the mean curvature and the scalar curvature of the boundary of any scalar flat conformal compactifications of Poincar{\'e}-Einstein manifolds. As a first consequence , we obtain a sharp lower bound…

In a compact, symplectic real manifold, i.e supporting an antisymplectic involution, we use Donaldson's construction to build a codimension 2 symplectic submanifold invariant under the action of the involution. If the real part of the…

We find a new obstruction for a real Einstein 4-orbifold with an A1-singularity to be a limit of smooth Einstein 4-manifolds. The obstruction is a curvature condition at the singular point. For asymptotically hyperbolic metrics, with…