The Variational Approach to Linear Boundary and Eigenvalue Problems
- 580 Downloads
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).
Unable to display preview. Download preview PDF.
- 6.1Achieser, H.T., Glasmann, T. M.: Theory of linear operators in Hilbert spaces. Pitman, Boston 1981Google Scholar
- 6.2Hirzebruch, F., Scharlau, W.: Einführung in die Funktionalanalysis. BI Taschenbücher 296, BI, Mannheim 1971Google Scholar
- 6.5Courant, R., Hilbert, D.: Methods of mathematical physics. Wiley-Interscience, New York 1966Google Scholar
- 6.7Lions, J.L., Magenes, E.: Non-homogeneous boundary value problems and applications. Springer, Berlin Heidelberg 1972Google Scholar