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.
Referenser
Allmänna 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 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 . . . . , 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 Kategori:Partiella differentialekvationer Kategori:Variationskalkyl