Anzeige
Erschienen in:
1985 | OriginalPaper | Buchkapitel
Compactness and Extremal Principles
verfasst von : Eberhard Zeidler
Erschienen in: Nonlinear Functional Analysis and its Applications
Verlag: Springer New York
Enthalten in: Professional Book Archive
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
In this chapter we give a far-reaching generalization of the following classical theorem of Weierstrass using compactness arguments: A continuous function F: [a, b] → ℝ, − oo < a < b < ∞, has a maximum and a minimum (see Fig. 38.1). Here, lower semicontinuous functionals and weak sequentially lower semicontinuous functionals play a crucial role. In this connection, we exploit, e.g., the fact that the continuity of F: [a, b] → ℝ is not needed for the existence of a minimum of F, but only the lower semicontinuity.