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Picard, R.

Randwertaufgaben in der verallgemeinerten Potentialtheorie. (German) Zbl 0466.31016

Math. Methods Appl. Sci. 3, 218-228 (1981).
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Cited in 24 Documents

MSC:

31C12 Potential theory on Riemannian manifolds and other spaces
58J32 Boundary value problems on manifolds
78A30 Electro- and magnetostatics

Keywords:

potential theory; electro-and magnetostatics; differential forms; Hilbert space methods; Dirichlet and Neumann boundary value problem; Hodge operator; Riemannian manifold; compact imbedding
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References:

[1] Agmon, Lectures on elliptic boundary value problems (1965)
[2] Aronszajn, A unique continuation theorem for exterior differential forms on Riemannian manifolds, Arkiv för Matematik 4 pp 34– (1961)
[3] Duff, Differential Forms in Manifolds with Boundary, Ann. of Math. 56 pp 115– (1952) · Zbl 0049.18804 · doi:10.2307/1969770
[4] Duff, Harmonic Tensors on Riemannian Manifolds with Boundary, Ann. of Math. 56 pp 128– (1952) · Zbl 0049.18901 · doi:10.2307/1969771
[5] Fichera, Teoria assiomatica delle forma armoniche, R. C. di Mat., Roma 20 pp 147– (1961)
[6] Friedrichs, Differential Forms on Riemannian Manifolds, Comm. Pure Appl. Math. 8 pp 551– (1955) · Zbl 0066.07504 · doi:10.1002/cpa.3160080408
[7] Gaffney, The harmonic operator for exterior differential forms, Proceedings of the Nationals Science, U.S.A. 37 pp 48– (1951) · Zbl 0042.10205 · doi:10.1073/pnas.37.1.48
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[11] Nécas, Les méthodes directes en théorie des equations elliptiques (1967)
[12] Picard , R. Ein Kompaktheitsresultat in der Theorie der verallgemeinerten Maxwell-Glei-chung
[13] Weber , C. Hilbertraummethoden zur Untersuchung der Beugung elektromagnetischer Wellen an Dielektrika 1977
[14] Weck, Maxwell’s Boundary Value Problem on Riemannian Manifolds with Nonsmooth Boundaries, J. Math. Anal. Appl. 46 pp 410– (1974) · Zbl 0281.35022 · doi:10.1016/0022-247X(74)90250-9
[15] Werner, Über das Verhalten elektromagnetischer Felder für kleine Frequenzen in mehrfach zusammenhängenden Gebieten I, Innenraumprobleme, J. Reine Angew. Math. 278/279 pp 365– (1976)
[16] Werner, Über das Verhalten elektromagnetischer Felder für kleine Frequenzen in mehrfach zusammenhängenden Gebieten II, Außenraumprobleme, J. Reine Angew. Math. 288 pp 98– (1976) · Zbl 0316.35034 · doi:10.1515/crll.1976.280.98
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