In this article we develop the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) for elliptic partial differential equations with inhomogeneous Dirichlet, Neumann, and Robin boundary conditions, high contrast property emerges from coefficients of operators conditions. By careful construction bases CEM-GMsFEM, introduce two which are used to handle Dirichlet ...

The Maslov index is used to compute the spectra of different boundary value problems for Schrödinger operators on compact manifolds. The main result is a spectral decomposition formula for a manifold M divided into components Ω1 and Ω2 by a separating hypersurface Σ. A homotopy argument relates the spectrum of a second-order elliptic operator on M to its Dirichlet and Neumann spectra on Ω1 and ...

This contribution deals with numerical realization of elliptic boundary value problems with unilateral boundary conditions using a fictitious domain method. Any fictitious domain formulation [2] extends the original problem defined in a domain ω to a new (fictitious) domainΩ with a simple geometry (e.g. a box) which contains ω . The main advantage consists in possibility to use a uniform mesh i...

This paper studies the local exact controllability and the local stabilization of the semilinear Schrödinger equation posed on a product of n intervals (n ≥ 1). Both internal and boundary controls are considered, and the results are given with periodic (resp. Dirichlet or Neumann) boundary conditions. In the case of internal control, we obtain local controllability results which are sharp as fa...

In this paper we show that the h-p spectral element method developed in [3,8,9] applies to elliptic problems in curvilinear polygons with mixed Neumann and Dirichlet boundary conditions provided that the Babuska–Brezzi inf–sup conditions are satisfied. We establish basic stability estimates for a non-conforming h-p spectral element method which allows for simultaneous mesh refinement and variab...

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...

This paper presents a Meyer–Vietoris type gluing formula for conformal invariant of Riemannian surface with boundary that is defined by the determinant Dirichlet-to-Neumann operator. The used to bound asymptotics under degeneration. It shown associated height function on moduli space hyperbolic surfaces geodesic proper only in genus zero. Properness implies compactness theorem Steklov isospectr...

We use the method of layer potentials to study interior and exterior Dirichlet and Neumann problems for the Helmholtz equation ((+k 2)u = 0 on a Lipschitz domain for all wave number k 2C with Im k 0. Following the approach for the case of smooth boundary 3], we pursue as solution a single layer potential for Neumann problem or a double layer potential for Dirichlet problem. The lack of smoothne...

We use the method of layer potentials to study interior and exterior Dirichlet and Neumann problems for the Helmholtz equation ( +k)u = 0 on a Lipschitz domain for all wave number k 2C with Imk 0. Following the approach for the case of smooth boundary [3], we pursue as solution a single layer potential for Neumann problem or a double layer potential for Dirichlet problem. The lack of smoothness...

The unique exact analytical solutions of parabolic boundary value prob-lems mathematical physics in piecewise homogeneous by the radial variable zwedge-shaped angular cylindrical-circular layer with a cavity were constructed at first time method classical integral and hybrid in-tegral transforms combination main (matrices influence Green matrices) proposed article.The cases assigning on verge w...