×

On generalized harmonic fields in domains with anisotropic nonhomogeneous media. (English) Zbl 0508.35024


MSC:

35F15 Boundary value problems for linear first-order PDEs
78A30 Electro- and magnetostatics
35C99 Representations of solutions to partial differential equations
35J55 Systems of elliptic equations, boundary value problems (MSC2000)
Full Text: DOI

References:

[1] Duvaut, G.; Lions, J. L., Inequalities in Mechanics and Physics (1976), Springer-Verlag: Springer-Verlag Berlin/Heidelberg/New York · Zbl 0331.35002
[2] Friedrichs, K. O., Differential forms on Riemannian manifolds, Comm. Pure Appl. Math., 8, 551-590 (1955) · Zbl 0066.07504
[3] Kress, R., Grundzüge einer Theorie der verallgemeinerten harmonischen Vektorfelder, Methoden und Verfahren der mathematischen Physik, (Brosowski, B.; Martensen, E., B. I.-Hochschulskripten 721/721a, Band 2 (1969), Bibliographisches Institut: Bibliographisches Institut Mannheim), 49-83 · Zbl 0195.11503
[4] Kress, R., Greensche Funktionen und Tensoren für verallgemeinerte harmonische Vektorfelder, Methoden und Verfahren der mathematischen Physik, (Brosowski, B.; Martensen, E., B. I.-Hochschulskripten 723 a/723b, Band 4 (1971), Bibliographisches Institut: Bibliographisches Institut Mannheim), 45-74 · Zbl 0227.31006
[5] Lions, J. L.; Magenes, E., Non-homogeneous Boundary Value Problems and Applications I (1972), Springer-Verlag: Springer-Verlag Berlin/Heidelberg/New York · Zbl 0223.35039
[6] Picard, R., Zur Theorie der zeitungabhängigen Maxwellschen Gleichungen mit der Randbedingung \(n\)(▽ × \(E) = n(▽ × \(H) = 0\) im inhomogenen anisotropen Medium, Bonner Math. Schriften, 65 (1973) · Zbl 0276.35076
[7] Saranen, J., Über die Approximation der Lösungen der Maxwellschen Randwertaufgabe mit der Methode der finiten Elemente, Appl. Anal., 10, 15-30 (1980) · Zbl 0454.65079
[8] Weber, Ch, A local compactness theorem for Maxwell’s equations, Math. Meth. Appl. Sci., 2, 11-25 (1980) · Zbl 0432.35032
[9] Weck, N., Maxwell’s boundary value problem on Riemann manifolds with nonsmooth boundaries, J. Math. Anal. Appl., 46, 410-437 (1974) · Zbl 0281.35022
[10] Wendland, W. L., Elliptic Systems in the Plane (1979), Pitman: Pitman London · Zbl 0396.35001
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.