zbMATH — the first resource for mathematics

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
Full Text: DOI
[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.