Boundary regularity for Maxwell's equations with applications to shape optimization

DOI10.1016/j.jde.2010.08.004zbMath1208.35144OpenAlexW2074362559MaRDI QIDQ619881

John Cagnol, Matthias M. Eller

Publication date: 18 January 2011

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2010.08.004

zbMATH Keywords

boundary value problemsMaxwell equationsshape optimization

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Optimization of shapes other than minimal surfaces (49Q10) Electromagnetic theory (general) (78A25) Maxwell equations (35Q61)

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Cites Work

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• On boundary regularity of solutions to Maxwell's equations with a homogeneous conservative boundary condition
• Shape derivative in the wave equation with Dirichlet boundary conditions
• Domain decomposition methods in optimal control of partial differential equations
• Symmetric hyperbolic systems with boundary conditions that do not satisfy the Kreiss–Sakamoto condition
• Initial-boundary value problems for hyperbolic equations with uniformly characteristic boundary
• Oriented Distance Function and Its Evolution Equation for Initial Sets with Thin Boundary
• L₂ is a continuable initial condition for kreiss' mixed problems