Document JFM 59.0503.02

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Condizioni sufficienti per la semicontinuità nel calcolo delle variazioni. (Italian) JFM 59.0503.02

Annali Pisa (2) 2, 41-58 (1933).

Der Verf. untersucht die Halbstetigkeit beim einfachsten Variationsproblem mit Doppelintegralen, und zwar für eine vorgegebene Fläche. Es gelingt ihm, mit Hilfe der \(\mathcal E\)-Funktion hinreichende Bedingungen für die Halbstetigkeit herzuleiten. Drei verschiedene Formen dieser Bedingungen werden angegeben; sie unterscheiden sich durch verschieden weitgehende Voraussetzungen über den Integranden des Variationsproblems, den Integrationsbereich und die Möglichkeit des Verschwindens der \(\mathcal E\)-Funktion.

Reviewer: Radon, J., Prof. (Breslau)

Cited in 1 Document

JFM Section:

Erster Halbband. Vierter Abschnitt. Analysis. Kapitel 15. Variationsrechnung.

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