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Singularities of eddy current problems. (English) Zbl 1170.35353

Summary: We consider the time-harmonic eddy current problem in its electric formulation where the conductor is a polyhedral domain. By proving the convergence in energy, we justify in what sense this problem is the limit of a family of Maxwell transmission problems: Rather than a low frequency limit, this limit has to be understood in the sense of A. Bossavit [Electromagnetism, in view of modeling. Mathématiques & Applications (Paris). 14. Paris: Springer-Verlag (1993; Zbl 0787.65090)]. We describe the singularities of the solutions. They are related to edge and corner singularities of certain problems for the scalar Laplace operator, namely the interior Neumann problem, the exterior Dirichlet problem, and possibly, an interface problem. These singularities are the limit of the singularities of the related family of Maxwell problems.

MSC:

35B65 Smoothness and regularity of solutions to PDEs
35R05 PDEs with low regular coefficients and/or low regular data
35Q60 PDEs in connection with optics and electromagnetic theory

Citations:

Zbl 0787.65090
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References:

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