Abstract
One of the first areas in which the basic variational concepts and methods are applied is the solution of large, important classes of linear boundary and eigenvalue problems. The results discussed in this chapter follow in part from the results on nonlinear boundary and eigenvalue problems which we shall discuss in Chap. 8; nonetheless we present proofs in this chapter which emphasise the simplicity and elementary character of the variational approach. We start with a variational proof of the spectral theorem for compact self-adjoint operators, followed by a general version of the projection theorem (for convex closed sets).
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Further Reading
Necas, J.: Les méthodes directes en théorie des équations elliptiques. Academia, Prague 1967
Rektory, K.: Variational methods in mathematics, science and engineering. Reidel, Dordrecht 1980
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© 1992 Springer-Verlag Berlin Heidelberg
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Blanchard, P., Brüning, E. (1992). The Variational Approach to Linear Boundary and Eigenvalue Problems. In: Variational Methods in Mathematical Physics. Texts and Monographs in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82698-6_7
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DOI: https://doi.org/10.1007/978-3-642-82698-6_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-82700-6
Online ISBN: 978-3-642-82698-6
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