Hilberts nittonde problem
Hilberts nittonde problem är ett av Hilberts 23 problem. Det formulerades år 1900 relaterat till frågan:

Är lösningarna till Lagranges ekvationer alltid analytiska?

Matematikern John Forbes Nash bevisade på 1950-talet att svaret på frågan är "ja": lösningarna är alltid analytiska.

Källor 
 
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. Reprinted in .
. "On the analiticity of extremals of multiple integrals" (English translation of the title) is a short research announcement disclosing the results detailed later in . While, according to the Complete list of De Giorgi's scientific publication (De Giorgi 2006, p. 6), an English translation should be included in , it is unfortunately missing.
. Translated in English as "On the differentiability and the analiticity of extremals of regular multiple integrals" in .
. Translated in English as "An example of discontinuous extremals for a variational problem of elliptic type" in .
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, translated in English as .
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 (reprinted as ), translated in English by Mary Frances Winston Newson as  (reprinted as ), and in French (with additions of Hilbert himself) by M. L. Laugel as .
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, translated in English as .
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19
Partiella differentialekvationer
Variationskalkyl
Hilberts nittonde problem är ett av Hilbertsproblem . Det formulerades årrelaterat till frågan : Är lösningarna till Lagranges ekvationer alltid analytiska ? Matematikern John Forbes Nash bevisade påtalet att svaret på frågan är "ja " : lösningarna är alltid analytiska . Källor . . Reprinted in\. . "On the analiticity of extremals of multiple integrals " ( English translation of the title ) is a short research announcement disclosing the results detailed later in\ . While , according to the Complete list of De Giorgi' s scientific publication ( De Giorgi p. an English translation should be included in , it is unfortunately missing . . Translated in English as "On the differentiability and the analiticity of extremals of regular multiple integrals" in\. . Translated in English as "An example of discontinuous extremals for a variational problem of elliptic type" in\. . . . translated in English as\. . . ( reprinted as ) , translated in English by Mary Frances Winston Newson as ( reprinted as ) , and in French ( with additions of Hilbert himself ) by M. L . Laugel as\. . translated in English as\. . . . . . . 19 Partiella differentialekvationer Variationskalkyl