Related papers: Dirichlet to Neumann Maps for Infinite Quantum Gra…
A general setup for deterministic system identification problems on graphs with Dirichlet and Neumann boundary conditions is introduced. When control nodes are available along the boundary, we apply a discretize-then-optimize method to…
We investigate the properties of certain elliptic systems leading, a~priori, to solutions that belong to the space of Radon measures. We show that if the problem is equipped with a so-called asymptotic Uhlenbeck structure, then the solution…
Quantum graphs and their experimental counterparts, microwave networks, are ideally suited to study the spectral statistics of chaotic systems. The graph spectrum is obtained from the zeros of a secular determinant derived from energy and…
We establish optimal L^p bounds for the nontangential maximal function of the gradient of the solution to a second order elliptic operator in divergence form, possibly non-symmetric, with bounded measurable coefficients independent of the…
R. M. Brown's theorem on mixed Dirichlet and Neumann boundary conditions is extended in two ways for the special case of polyhedral domains. A (1) more general partition of the boundary into Dirichlet and Neumann sets is used on (2)…
In this paper we study upper and lower bounds of the index and the nullity for sequences of harmonic maps with uniformly bounded Dirichlet energy from a two-dimensional Riemann surface into a compact target manifold. The main difficulty…
We study a class of fractional semilinear elliptic equations and formulate the corresponding Calder\'on problem. We determine the nonlinearity from the exterior partial measurements of the Dirichlet-to-Neumann map by using first order…
We consider initial-boundary value problems for the KdV equation $u_t + u_x + 6uu_x + u_{xxx} = 0$ on the half-line $x \geq 0$. For a well-posed problem, the initial data $u(x,0)$ as well as one of the three boundary values $\{u(0,t),…
We consider the Dirichlet-to-Neumann mapping and the Neumann problem for the Laplace operator on a torus, given in toroidal coordinates. The Dirichlet-to-Neumann mapping is expressed with respect to series expansions in toroidal harmonics…
We consider the Dirichlet-to-Neumann operator associated to a strictly elliptic operator on the space $\mathrm{C}(\partial M)$ of continuous functions on the boundary $\partial M$ of a compact manifold $\overline{M}$ with boundary. We prove…
In this paper we investigate elliptic partial differential equations on Lipschitz domains in the plane whose coefficient matrices have small (but possibly nonzero) imaginary parts and depend only on one of the two coordinates. We show that…
We study Neumann functions for divergence form, second order elliptic systems with bounded measurable coefficients in a bounded Lipschitz domain or a Lipschitz graph domain. We establish existence, uniqueness, and various estimates for the…
In this work, we construct and quantify asymptotically in the limit of large mass a variety of edge-localized stationary states of the focusing nonlinear Schr\"odinger equation on a quantum graph. The method is applicable to general bounded…
We propose a new numerical method to reconstruct the isotropic electrical conductivity from measured restricted Dirichlet-to-Neumann map data in electrical impedance tomography (EIT) model. "Restricted Dirichlet-to-Neumann (DtN) map data"…
This work considers properties of the Neumann-to-Dirichlet map for the conductivity equation under the assumption that the conductivity is identically one close to the boundary of the examined smooth, bounded and simply connected domain. It…
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…
We prove \emph{global} uniqueness for an inverse problem for the fractional conductivity equation on domains that are bounded in one direction. The conductivities are assumed to be isotropic and nontrivial in the exterior of the domain,…
We derive a priori second order estimates for solutions of a class of fully nonlinear elliptic equations on Riemannian manifolds under some very general structure conditions. We treat both equations on closed manifolds, and the Dirichlet…
Recent work of the authors and their collaborators has uncovered fundamental connections between the Dirichlet-to-Neumann map, the spectral flow of a certain family of self-adjoint operators, and the nodal deficiency of a Laplacian…
For a compact Riemannian surface $(M,g)$ with non-empty boundary $\Gamma$, the Dirichlet-to-Neumann operator (DtN-map) $\Lambda_g:C^\infty(\Gamma)\to C^\infty(\Gamma)$ is defined by $\Lambda_gf=\left.\frac{\partial…