EXISTENCE, UNIQUENESS AND REGULARITY FOR SOLUTIONSV OF THE CONICAL DIFFRACTION PROBLEM

DOI10.1142/S0218202500000197zbMath1010.78008OpenAlexW1964791778MaRDI QIDQ4798795

Johannes Elschner, Rainer Hinder, Frank Penzel, Gunther Schmidt

Publication date: 16 March 2003

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218202500000197

zbMATH Keywords

transmission conditionsexistence and uniqueness resultsHelmholtz equations in \(R^2\)leading asymptotics near the edgesstrongly elliptic variational formulation

Mathematics Subject Classification ID

Diffraction, scattering (78A45) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (12)

The problem of scattering by a mixture of cracks and obstacles ⋮ A posteriori error analysis for the conical diffraction problem ⋮ Shape derivatives in Kondratiev spaces for conical diffraction ⋮ Conical diffraction by multilayer gratings: a recursive integral equation approach. ⋮ Analytical investigation of an integral equation method for electromagnetic scattering by biperiodic structures ⋮ Domain decomposition method for Maxwell's equations: scattering off periodic structures ⋮ Integral equations for conical diffraction by coated grating ⋮ Regularity for Maxwell eigenproblems in photonic crystal fibre modelling ⋮ The direct electromagnetic scattering problem from an imperfectly conducting cylinder at oblique incidence ⋮ Variational approach to scattering of plane elastic waves by diffraction gratings ⋮ The method of boundary integral equations for a mixed scattering problem ⋮ Mathematical analysis of scattering problems for partially coated obstacles and cracks

Cites Work

• A direct boundary integral equation method for transmission problems
• A coercive bilinear form for Maxwell's equations
• Numerical analysis of diffraction by periodic structures: \(TM\) polarization
• Maxwell's Equations in a Periodic Structure
• Singularities of Maxwell interface problems
• Integral Equation Methods in a Quasi-Periodic Diffraction Problem for the Time-Harmonic Maxwell’s Equations
• Solution of a boundary value problem for the Helmholtz equation via variation of the boundary into the complex domain
• Diffraction in periodic structures and optimal design of binary gratings. Part I: direct problems and gradient formulas
• Guided waves by electromagnetic gratings and non‐uniqueness examples for the diffraction problem
• Optimal design of periodic antireflective structures for the Helmholtz equation
• Variational Approximation of Maxwell's Equations in Biperiodic Structures
• A variational method for electromagnetic diffraction in biperiodic structures
• Finite Element Approximation of Time Harmonic Waves in Periodic Structures

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