Related papers: Unique determination of a Kato class potential fro…

This paper is devoted to the problem of recovering a potential $q$ in a domain in $\mathbb{R}^d$ for $d \geq 3$ from the Dirichlet to Neumann map. This problem is related to the inverse Calder\'on conductivity problem via the Liouville…

We consider the quasi-linear eigenvalue problem $-\Delta_p u = \lambda g(u)$ subject to Dirichlet boundary conditions on a bounded open set $\Omega$, where $g$ is a locally Lipschitz continuous functions. Imposing no further conditions on…

We consider an inverse spectral problem for radial Schr\"odinger operators with singular potentials. First, we show that the knowledge of the Dirichlet spectra for infinitely many angular momenta~$\ell$ satisfying a M\"untz-type condition…

We show that the knowledge of the set of the Cauchy data on the boundary of a $C^1$ bounded open set in $\R^n$, $n\ge 3$, for the Schr\"odinger operator with continuous magnetic and bounded electric potentials determines the magnetic field…

We consider initial boundary value problems for one-dimensional diffusion equation with time-fractional derivative of order $\alpha \in (0,1)$ which are subject to non-zero Neumann boundary conditions. We prove the uniqueness for an inverse…

We consider the inverse problem of determining the time independent scalar potential of the dynamic Schr\"odinger equation in an infinite cylindrical domain, from one Neumann boundary observation of the solution. Assuming that this…

We extend the method of layer potentials to manifolds with boundary and cylindrical ends. To obtain this extension along the classical lines, we have to deal with several technical difficulties due to the non-compactness of the boundary,…

On a compact Riemannian manifold $M$ with boundary $Y$, we express the log of the zeta-determinant of the Dirichlet-to-Neumann operator acting on $q$-forms on $Y$ as the difference of the log of the zeta-determinant of the Laplacian on…

This paper considers to the problems of diffraction of electromagnetic waves on a half-plane, which has a finite inclusion in the form of a Lipschitz curve. The diffraction problem formulated as boundary value problem for Helmholtz…

We study the existence of solutions of the Dirichlet problem for the Schroedinger operator with measure data $$ \left\{ \begin{alignedat}{2} -\Delta u + Vu & = \mu && \quad \text{in } \Omega,\\ u & = 0 && \quad \text{on } \partial \Omega.…

We prove for a two dimensional bounded domain that the Cauchy data for the Schroedinger equation measured on an arbitrary open subset of the boundary determines uniquely the potential. This implies, for the conductivity equation, that if we…

We study self-similar solutions of a multi-phase Stefan problem for a heat equation on the half-line $x>0$ with a constant initial data and with Dirichlet or Neumann boundary conditions. In the case of Dirichlet boundary condition we prove…

We consider Sturm-Liouville operators on the line segment [0, 1] with general regular singular potentials and separated boundary conditions. We establish existence and a formula for the associated zeta-determinant in terms of the Wronski-…

This paper presents a Meyer-Vietoris type gluing formula for a conformal invariant of a Riemannian surface with boundary that is defined by the determinant of the Dirichlet-to-Neumann operator. The formula is used to bound the asymptotics…

We prove that a potential $q$ can be reconstructed from the Dirichlet-to-Neumann map for the Schrodinger operator $-\Delta_g + q$ in a fixed admissible 3-dimensional Riemannian manifold $(M,g)$. We also show that an admissible metric $g$ in…

In this paper, we consider the wave equation for the Laplace operator with potential, initial data, and nonhomogeneous Dirichlet boundary condition. We establish a weak solution by using traces and extension domains. We also establish the…

We consider uniqueness in an inverse Schr\"odinger problem in a bounded domain in $\mathbb{R}^2$ given the Dirichlet-to-Neumann map on part of the boundary. On the remaining boundary we impose a new type of singular boundary condition with…

In this work, we investigate the discrete Calder\'{o}n problem on grid graphs of dimension three or higher, formed by hypercubic structures. The discrete Calder\'{o}n problem is concerned with determining whether the discrete…

We show that measurements of the Neumann-to-Dirichlet map, roughly speaking, on a certain part of the boundary of a smooth domain in dimension 3 or higher, for inputs with support restricted to the other part, determine an electric…

We study the boundary behavior of solutions to the Dirichlet problems for integro-differential operators with order of differentiability $s \in (0, 1)$ and summability $p>1$. We establish a nonlocal counterpart of the Wiener criterion,…