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Regularity theorems for Maxwell’s equations. (English) Zbl 0477.35020


MSC:

35B65 Smoothness and regularity of solutions to PDEs
35G15 Boundary value problems for linear higher-order PDEs
78A25 Electromagnetic theory (general)
35Q99 Partial differential equations of mathematical physics and other areas of application
78A45 Diffraction, scattering
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References:

[1] Agmon, Lectures on Elliptic Boundary Value Problems (1965)
[2] Leis, Zur Theorie der zeitunabhängigen Maxwellschen Gleichungen, Gesellsch. f. Mathematik u. Datenverarb. Bonn Nr. 50 (1971) · Zbl 0227.35077
[3] Lions, Inequalities in Mechanics and Physics (1976)
[4] Müller, Grundprobleme der mathematischen Theorie elektromagnetischer Schwingungen (1957) · Zbl 0087.21305
[5] Picard , R. Zur Existenz des Wellenoperators bei Anfangsrandwertproblemen vom Maxwell-Typ 1977 · Zbl 0346.35087
[6] Weber , C. Hilbertraummethoden zur Untersuchung der Beugung elektromagnetischer Wellen an Dielektrika 1977
[7] Weber, A Local Compactness Theorem for Maxwell’s Equations, Math. Meth. in the Appl. Sci. 2 pp 12– (1980) · Zbl 0432.35032
[8] Weck, Maxwell’s boundary value problem on Riemannian manifolds with smooth boundaries, J. Math. Anal. Appl. 46 pp 410– (1974) · Zbl 0281.35022
[9] Werner, On the exterior boundary value problem of perfect reflection for stationary electromagnetic wave fields, J. Math. Anal. Appl. 7 pp 348– (1963) · Zbl 0118.43501
[10] Werner, Randwertprobleme für die zeitunabhängigen Maxwellschen Gleichungen mit variablen Koeffizienten, Arch. Rat. Mech. An. 18 (3) pp 167– (1965) · Zbl 0142.37501
[11] Willmore, An Introduction to Differential Geometry (1969) · Zbl 0086.14401
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