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...

We prove (in superspace) the equivalence between the higher-derivative N = 1 supergravity, defined by a holomorphic function F of the chiral scalar curvature superfield, and the standard theory of a chiral scalar superfield with a chiral superpotential W , coupled to the (minimal) Poincaré supergravity in four spacetime dimensions. The relation between the holomorphic functions F and W is found...

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 ...

We demonstrate that solving the classical problems mentioned in the title on quadrature domains when the given boundary data is rational is as simple as the method of partial fractions. A by-product of our considerations will be a simple proof that the Dirichlet-to-Neumann map on a double quadrature domain sends rational functions on the boundary to rational functions on the boundary. The resul...

In this report I give the short historical review some of the first steps that were done to the invention of SUSY in Kharkov team headed by D.Volkov. This paper is dedicated to the memory of Prof. Yu. Gol'fand, whose ideas of SUSY inspired the most active developments in High Energy Physics over thirty years. " Geometry of space is associated with mathematical group " Felix Klein , " Erlagen Pr...