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On the Relation between the S-matrix and the Spectrum of the Interior Laplacian

A. G. Ramm (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

The main results of this paper are: 1) a proof that a necessary condition for 1 to be an eigenvalue of the S-matrix is real analyticity of the boundary of the obstacle, 2) a short proof that if 1 is an eigenvalue of the S-matrix, then k² is an eigenvalue of the Laplacian of the interior problem, and that in this case there exists a solution to the interior Dirichlet problem for the Laplacian, which admits an analytic continuation to the whole space ℝ³ as an entire function.

On time-harmonic Maxwell equations with nonhomogeneous conductivities: Solvability and FE-approximation

Michal Křížek, Pekka Neittaanmäki (1989)

Aplikace matematiky

The solvability of time-harmonic Maxwell equations in the 3D-case with nonhomogeneous conductivities is considered by adapting Sobolev space technique and variational formulation of the problem in question. Moreover, a finite element approximation is presented in the 3D-case together with an error estimate in the energy norm. Some remarks are given to the 2D-problem arising from geophysics.

On uniqueness in electromagnetic scattering from biperiodic structures

Armin Lechleiter, Dinh-Liem Nguyen (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Consider time-harmonic electromagnetic wave scattering from a biperiodic dielectric structure mounted on a perfectly conducting plate in three dimensions. Given that uniqueness of solution holds, existence of solution follows from a well-known Fredholm framework for the variational formulation of the problem in a suitable Sobolev space. In this paper, we derive a Rellich identity for a solution to this variational problem under suitable smoothness conditions on the material parameter. Under additional...

Optical leptons.

Kovachev, Lubomir M. (2004)

International Journal of Mathematics and Mathematical Sciences

Optimal multiphase transportation with prescribed momentum

Yann Brenier, Marjolaine Puel (2002)

ESAIM: Control, Optimisation and Calculus of Variations

A multiphase generalization of the Monge–Kantorovich optimal transportation problem is addressed. Existence of optimal solutions is established. The optimality equations are related to classical Electrodynamics.

Optimal Multiphase Transportation with prescribed momentum

Yann Brenier, Marjolaine Puel (2010)

ESAIM: Control, Optimisation and Calculus of Variations

A multiphase generalization of the Monge–Kantorovich optimal transportation problem is addressed. Existence of optimal solutions is established. The optimality equations are related to classical Electrodynamics.

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