A remark on the regularity of solutions of Maxwell’s equations on Lipschitz domains. (English) Zbl 0699.35028

Costabel, Martin

Math. Methods Appl. Sci. 12, No. 4, 365-368 (1990).

The following theorem is proved: Let u satisfy the conditions \[ (1)\quad u\in L^ 2(\Omega),\quad div u\in L^ 2(\Omega),\quad curl u\in L^ 2(\Omega)\quad in\quad \Omega \] and either (2) \(n\times u\in L^ 2(\Gamma)\) or (3) \(n\cdot u\in L^ 2(\Gamma)\) then \(u\in H^{1/2}(\Omega)\). If (1) is satisfied, then the two conditions (2) and (3) are equivalent.

Reviewer: H.Benker

MSC:

35B65	Smoothness and regularity of solutions to PDEs
35K55	Nonlinear parabolic equations

Keywords:

Maxwell’s equations; Lipschitz domains

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