Related papers: Embedding transmission problems for Maxwell's equa…
We study the limiting absorption principle and the well-posedness of Maxwell equations with anisotropic sign-changing coefficients in the time-harmonic domain. The starting point of the analysis is to obtain Cauchy problems associated with…
In this paper, we study the regularity of the solutions of Maxwell's equations in a bounded domain. We consider several different types of low regularity assumptions to the coefficients which are all less than Lipschitz. We first develop a…
This paper is devoted to establishing results for semilinear elliptic boundary value problems where the solvability of problems subject to {\it No Flux} boundary conditions follows from the solvability of related {\it Dirichlet} boundary…
This paper is concerned with the mathematical analysis of the time-domain electromagnetic scattering problem in an infinite rectangular waveguide. A transparent boundary condition is developed to reformulate the problem into an equivalent…
We present boundary-integral equations for Maxwell-type problems in a differential-form setting. Maxwell-type problems are governed by the differential equation $(\delta\mathrm{d}-k^2)\omega = 0$, where $k\in\mathbb{C}$ holds, subject to…
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…
Parameter-elliptic boundary-value problems are investigated on the extended Sobolev scale. This scale consists of all Hilbert spaces that are interpolation spaces with respect to the Hilbert Sobolev scale. The latter are the H\"ormander…
In this paper second order elliptic boundary value problems on bounded domains $\Omega\subset\dR^n$ with boundary conditions on $\partial\Omega$ depending nonlinearly on the spectral parameter are investigated in an operator theoretic…
The Maxwell's equations are solved when it has an inhomogeneous terms as a source. The solution is very general in a sense that it handles arbitrary current source and anisotropic media. The calculation is carried out in the k-domain after…
In this paper we study a class of elliptic boundary hemivariational inequalities which originates in the steady-state heat conduction problem with nonmonotone multivalued subdifferential boundary condition on a portion of the boundary…
In the first part of the article, we give necessary and sufficient conditions for the solvability of a class of nonlinear elliptic boundary value problems with nonlinear boundary conditions involving the q-Laplace-Beltrami operator. In the…
The Maxwell equations for the spherical components of the electromagnetic fields outside sources do not separate into equations for each component alone. We show, however, that general solutions can be obtained by separation of variables in…
In this paper, we prove the a priori estimates for two-dimensional second order homogeneous linear elliptic equations in a narrow region. In a crescent-shaped area, part of the boundary is subject to an oblique derivative boundary…
This paper is concerned with weighted energy estimates and diffusion phenomena for the initial-boundary problem of the wave equation with space-dependent damping term in an exterior domain. In this analysis, an elliptic problem was…
As is known, tetrahedron equations lead to the commuting family of transfer-matrices and provide the integrability of corresponding three-dimensional lattice models. We present the modified version of these equations which give the…
Rapid growth of constraints is often observed in free evolutions of highly gravitating systems. To alleviate this problem we investigate the effect of adding spatial derivatives of the constraints to the right hand side of the evolution…
We propose and analyze an efficient spectral-Galerkin approximation for the Maxwell transmission eigenvalue problem in spherical geometry. Using a vector spherical harmonic expansion, we reduce the problem to a sequence of equivalent…
In the present article, we study the diffusion equations with fractional time derivatives. The aim of this paper is to investigate the best possible regularity for the initial value/boundary value problems with non-homogeneous Dirichlet…
We propose a new class of fundamental solutions for the numerical analysis of boundary value problems for the Maxwell equations. We prove completeness of systems of such fundamental solutions in appropriate Sobolev spaces on a smooth…
In this paper, we present results about the existence and uniqueness of solutions of elliptic equations with transmission and Wentzell boundary conditions. We provide Schauder estimates and existence results in H\"older spaces. As an…