Über die Variationsrechnung in Hilberts Werken zur Analysis


Abstract
The paper deals with some of the developments in analysis against the background of Hilbert's contributions to the Calculus of Variations. As a starting point the transformation is chosen that took place at the end of the 19th century in the Calculus of Variations, and emphasis is placed on the influence of Dirichlet's principle. The proof of the principle (the resuscitation ) led Hilbert to questions arising in the 19th and 20th problems of his famous Paris address in 1900: theexistence in a generalized sense, and theregularity of solutions of elliptic partial differential equations. By this new concept Hilbert pointed out two very important issues the history of which is closely tied up with the rise of modern analysis. Further on, Hilbert'stheorem of independence of the Calculus of Variations, an important contribution to its formal apparatus as well as to its field theory, is briefly discussed. But even as Hilbert published his first essential results, he was turning his attention to another area of mathematics that differs in an important respect from the Calculus of Variations:integral equations. Hilbert did so because he recognized that in this branch by its flexibility he was coming closer to his goal of an unifying methodological approach to analysis
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1007/BF02913642
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Translate to english
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 42,993
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

The Principle of Least Action as the Logical Empiricist's Shibboleth.Michael Stöltzner - 2002 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 34 (2):285-318.

Add more citations

Similar books and articles

Aspekte der frege–hilbert-korrespondenz.Kai F. Wehmeier - 1997 - History and Philosophy of Logic 18 (4):201-209.
Hilberts Logik. Von der Axiomatik zur Beweistheorie.Volker Peckhaus - 1995 - NTM Zeitschrift für Geschichte der Wissenschaften, Technik und Medizin 3 (1):65-86.
Hilbert's Programs: 1917–1922.Wilfried Sieg - 1999 - Bulletin of Symbolic Logic 5 (1):1-44.
Extensions of the Finitist Point of View.Matthias Schirn & Karl-Georg Niebergall - 2001 - History and Philosophy of Logic 22 (3):135-161.
Hilbert's Program Then and Now.Richard Zach - 2007 - In Dale Jacquette (ed.), Philosophy of Logic. Amsterdam: North Holland. pp. 411–447.
The Frege-Hilbert Controversy.Patricia Blanchette - 2007 - The Stanford Encyclopedia of Philosophy.

Analytics

Added to PP index
2010-09-01

Total views
12 ( #639,595 of 2,259,503 )

Recent downloads (6 months)
2 ( #663,859 of 2,259,503 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature