Hilbert's nineteenth problem
- Hilbert's nineteenth problem
Hilbert's nineteenth problem is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. It asks whether the solutions of Lagrangians are always analytic. Sergei Natanovich Bernstein showed the answer is yes [ [http://www.google.com/search?q=cache:CwmHuzVyHV4J:philsci-archive.pitt.edu/archive/00001225/01/wilson9archive.doc+%22Serge+Bernstein%22+19th+hilbert+problem&hl=it&ct=clnk&cd=6&gl=it 403 Forbidden ] ] in his doctoral dissertation submitted to the Sorbonne in 1904, subject to some additional hypotheses.
However, it is widely known that the answer was shown to be yes by Ennio de Giorgi in 1957, and, independently and using different methods, by John Forbes Nash [http://www.cs.math.ist.utl.pt/cim.www/cimE/boletins/number12/35.pdf] .
Notes
External links
* An Italian PhD course about the subject: [http://siba2.unile.it/ese/search/issue.php?recs=10&id=656&pub_type=m&single_pub=1&pub_id=284&n_campo=contents]
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