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Scattering problems in a domain with small holes.

V. Chiadò Piat, M. Codegone (2003)

RACSAM

In this paper, we consider a family of scattering problems in perforated unbounded domains Ωε. We assume that the perforation is contained in a bounded region and that the holes have a ?critical? size. We study the asymptotic behaviour of the outgoing solutions of the steady-state scattering problem and we prove that an extra term appears in the limit equation. Finally, we obtain convergence results for scattering frequencies and solutions.

Singularities of Maxwell interface problems

Martin Costabel, Monique Dauge, Serge Nicaise (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We investigate time harmonic Maxwell equations in heterogeneous media, where the permeability μ and the permittivity ε are piecewise constant. The associated boundary value problem can be interpreted as a transmission problem. In a very natural way the interfaces can have edges and corners. We give a detailed description of the edge and corner singularities of the electromagnetic fields.

Singularities of Maxwell’s system in non-hilbertian Sobolev spaces

Wided Chikouche, Serge Nicaise (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We study the regularity of the solution of the regularized electric Maxwell problem in a polygonal domain with data in L p ( Ω ) 2 . Using a duality method, we prove a decomposition of the solution into a regular part in the non-Hilbertian Sobolev space W 2 , p ( Ω ) 2 and an explicit singular one.

Solvability of a first order system in three-dimensional non-smooth domains

Michal Křížek, Pekka Neittaanmäki (1985)

Aplikace matematiky

A system of first order partial differential equations is studied which is defined by the divergence and rotation operators in a bounded nonsmooth domain Ω 𝐑 3 . On the boundary δ Ω , the vanishing normal component is prescribed. A variational formulation is given and its solvability is investigated.

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