Costabel, Martin A remark on the regularity of solutions of Maxwell’s equations on Lipschitz domains. (English) Zbl 0699.35028 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 Cited in 102 Documents MSC: 35B65 Smoothness and regularity of solutions to PDEs 35K55 Nonlinear parabolic equations Keywords:Maxwell’s equations; Lipschitz domains PDF BibTeX XML Cite \textit{M. Costabel}, Math. Methods Appl. Sci. 12, No. 4, 365--368 (1990; Zbl 0699.35028) Full Text: DOI References: [1] Costable, SIAM J. Math. Anal. 19 pp 613– (1988) [2] and , Finite Element Methods for Navier-Stokes Equations. Springer-Verlag. Berlin, 1986. · Zbl 0585.65077 · doi:10.1007/978-3-642-61623-5 [3] Boundary Value Problems in Non-Smooth Domains. Pitman, London, 1985. [4] Jerison, Bull Amer. Math. Soc. 4 pp 203– (1981) [5] and , ’Boundary value problems on Lipschitz domains’, in (ed.), Studies in Partial Differential Equations. MAA Studies in Mathematics 23, pages 1-68. Math. Assoc. of America, Washington, D.C. 1982. [6] Initial Boundary Value Problems in Mathematical Physics, Wiley, Chichester, 1986. · Zbl 0599.35001 · doi:10.1007/978-3-663-10649-4 [7] Les Méthodes Directes en Théorie des Equations Elliptiques, Masson, Paris, 1967. [8] Picard, Math. Z. 187 pp 151– (1984) [9] Weber, Math. Meth. Appl. Sci. 2 pp 12– (1980) [10] Weck, J. Math. Anal. Appl. 46 pp 410– (1974) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.