Related papers: The Neumann isospectral problem for trapezoids

The purpose of this paper is to prove the uniqueness theorem of solutions of eigenvalue equations on one end of Riemannian manifolds for drift Laplacians, including the standard Laplacian as a special case; we shall impose "a sort of…

We consider the inverse problem of determining the Lam\'{e} parameters and the density of a three-dimensional elastic body from the local time-harmonic Dirichlet-to-Neumann map. We prove uniqueness and Lipschitz stability of this inverse…

This paper is concerned with the inverse diffraction problems by a periodic curve with Dirichlet boundary condition in two dimensions. It is proved that the periodic curve can be uniquely determined by the near-field measurement data…

We give a classification of non-Abelian T-duals of the flat metric in D=4 dimensions with respect to the four-dimensional continuous subgroups of the Poincare group. After dualizing the flat background, we identify majority of dual models…

Let $(X,g)$ be a compact manifold with conic singularities. Taking $\Delta_g$ to be the Friedrichs extension of the Laplace-Beltrami operator, we examine the singularities of the trace of the half-wave group $e^{- i t \sqrt{…

We consider the spectral problems for the Sturm-Liouville operator generated by the Dirichlet, Neumann, Dirichlet-Neumann and Neumann-Dirichlet conditions. The necessary and sufficient condition for the coincidence of the spectrum of the…

We consider well-posedness of the boundary value problem in presence of an inclusion with complex conductivity $k$. We first consider the transmission problem in $\mathbb{R}^d$ and characterize solvability of the problem in terms of the…

Two planar embedded circle patterns with the same combinatorics and the same intersection angles can be considered to define a discrete conformal map. We show that two locally finite circle patterns covering the unit disc are related by a…

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 article uncoditional solvability of the Carleman-Vekua equation with a singular point is proved, the Riemann-Hilbert problem is solved integral representations of solutions, the strictures of their zeros and poles are recieved.

We study a one-dimensional one-phase Stefan problem with a Neumann boundary condition on the fixed part of the boundary. We construct the unique self-similar solution, and show that starting from arbitrary initial data, solution orbits…

\AA. Pleijel (1956) has proved that in the case of the Laplacian with Dirichlet condition, the equality in the Courant nodal theorem (Courant sharp situation) can only be true for a finite number of eigenvalues when the dimension is $\geq…

We consider compact metric graphs with an arbitrary self adjoint realisation of the differential Laplacian. After discussing spectral properties of Laplacians, we prove several versions of trace formulae, relating Laplace spectra to sums…

The paper contains a stability analysis of the plane-wave Riemann problem for the two-dimensional hyperbolic conservation laws for an ideal compressible gas. It is proved that the contact discontinuity in the plane-wave Riemann problem is…

We state that any constant curvature Riemannian metric with conical singularities of constant sign curvature on a compact (orientable) surface $S$ can be realized as a convex polyhedron in a Riemannian or Lorentzian) space-form. Moreover…

We consider the spectral Neumann problem for the Laplace operator in an acoustic waveguide $\Pi_{l}^{\varepsilon}$ obtained from a straight unit strip by a low box-shaped perturbation of size $2l\times\varepsilon,$ where $\varepsilon>0$ is…

We present multiplicity results for the periodic and Neumann-type boundary value problems associated with coupled Hamiltonian systems. For the periodic problem, we couple a system having twist condition with another one whose nonlinearity…

Under some non-invertibility and irreducibility condition, for nilmanifold Anosov maps with one-dimensional stable bundle, we get the equivalence among the existence of invariant unstable bundle, the existence of topological conjugacy to…

The relevance of the data concerning upward--going muons for the solution of the atmospheric neutrino problem is stressed. In particular, their inclusion in the analysis confirms the goodness of the neutrino oscillation hypothesis and…

Let $M$ be a strongly pseudoconvex complex manifold which is also the total space of a principal $G$-bundle with $G$ a Lie group and compact orbit space $\bar M/G$. Here we investigate the $\bar\partial$-Neumann Laplacian on $M$. We show…