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Digitale Medien

Zwei Klassen vollständiger Funktionensysteme zur Behandlung der Randwertaufgaben der Schwingungsgleichung ΔU + k2U = 0 (1980)

Müller, C. ; Kersten, H. ; Leis, R.

Chichester, West Sussex : Wiley-Blackwell

Mathematical Methods in the Applied Sciences 2 (1980), S. 48-67

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Details

ISSN: 0170-4214

Schlagwort(e): Mathematics and Statistics ; Applied Mathematics

Quelle: Wiley InterScience Backfile Collection 1832-2000

Thema: Mathematik

Notizen: In this paper we present new methods to solve the classical Dirichlet and Neumann problems for ΔU + k2U = 0. We prove that the solutions of this equation for a region S containing G restricted to G are dense in L2(∂G). Introducing a basis in the space of solutions for S we find a complete orthogonal system in L2(∂G) which can be used to solve the boundary value problems by means of approximation in the Hilbertspace norm. Regularity estimates lead to series expansions in G.The well-known basis systems obtained by separation of variables thus may be used for every regular region without the very special geometric restrictions. Another class of basis systems may be obtained in analogy to the Runge. theorems by considering types of singularity functions.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1002/mma.1670020106

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