We prove wavenumber-explicit bounds on the Dirichlet-to-Neumann map for the Helmholtz equation in the exterior of a bounded obstacle when one of the following three conditions holds: (i) the exterior of the obstacle is smooth and nontrapping, (ii) the obstacle is a nontrapping polygon, (iii) the obstacle is star-shaped and Lipschitz. We prove bounds on the Neumann-to-Dirichlet map when one of c...

We consider the inverse problem for the second order self-adjoint hyperbolic equation in a bounded domain in R n with lower order terms depending analytically on the time variable. We prove that, assuming the BLR condition, the time-dependent Dirichlet-to-Neumann operator prescribed on a part of the boundary uniquely determines the coefficients of the hyperbolic equation up to a diffeomorphism ...

Within front-form dynamics and in the Breit frame where initial and final three-momenta of the system are directed along the z axis, Poincaré covariance constrains the current operator only through kinematical rotations around the z axis. Therefore, in this frame the current can be taken in the one-body form. Applications to deep inelastic structure functions in an exactly solvable model and to...

We consider the inverse problem for the second order hyperbolic equation in a bounded domain in R n with lower order terms depending analytically on the time variable. We prove that the time-dependent Dirichlet-to-Neumann operator prescribed on a part of the boundary uniquely determines the coefficients of the hyperbolic equation up to a diffeomorphism and a gauge transformation.

We will study a class of Steklov-Neumann boundary value problems for some quasilinear elliptic equations. We obtain result ensuring the existence of solutions when resonance and nonresonance conditions occur. The result was obtained by using variational arguments.

Given a closed manifold M and connected submanifold \(N\subset M\) of positive codimension, we study the Steklov spectrum domain \(\varOmega _\varepsilon \subset obtained by removing tubular neighborhood size \(\varepsilon \) around N. All nonzero eigenvalues in mid-frequency range tend to infinity at rate which depends only on codimension N M. Eigenvalues above are also described: they followi...

In this paper, we obtain a Lichnerowicz-type estimate for the first positive Steklov eigenvalues on graphs and discuss its rigidity.

Domain decomposition methods are designed to deal with coupled or transmission problems for partial differential equations. Since the original boundary value problem is replaced by local problems in substructures, domain decomposition methods are well suited for both parallelization and coupling of different discretization schemes. In general, the coupled problem is reduced to the Schur complem...

Abstract. We consider the inverse boundary value problem for the system of equations describing elastic waves in isotropic media on a bounded domain in R via a finite-time Laplace transform. The data is the dynamical Dirichlet-to-Neumann map. More precisely, using the full symbol of the transformed Dirichlet-to-Neumann map viewed as a semiclassical pseudodifferential operator, we give an explic...

for every rational function ƒ with poles off K. In this note it is shown that any operator for which the spectrum is a spectral set has a nontrivial invariant subspace. In [6] von Neumann introduced the notion of spectral set and showed that if T has II T\\ = 1 then the closed unit disc, D"~, is a spectral set for T. For this reason any operator whose spectrum is a spectral set is called a von ...