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

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


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