Ennio de Giorgi

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Ennio De Giorgi
Ennio de Giorgi.jpg
Born (1928-02-08)8 February 1928
Died 25 October 1996(1996-10-25) (aged 68)
Nationality Italian
Alma mater Sapienza University of Rome
Known for theory of Caccioppoli sets, solution of 19th Hilbert problem, existence and regularity theorem for minimal surfaces
Awards
Scientific career
Fields Calculus of variations, Partial differential equations
Institutions Scuola Normale Superiore di Pisa
Doctoral advisor Mauro Picone
Doctoral students

Ennio De Giorgi (8 February 1928 – 25 October 1996) was an Italian mathematician, member of the House of Giorgi, who worked on partial differential equations and the foundations of mathematics.

Mathematical work

He solved Bernstein's problem about minimal surfaces.

He solved the 19th Hilbert problem on the regularity of solutions of elliptic partial differential equations.

Quotes

  • "If you can't prove your theorem, keep shifting parts of the conclusion to the assumptions, until you can" [1]

Selected publications

Articles

Scientific papers

  • De Giorgi, Ennio (1953), "Definizione ed espressione analitica del perimetro di un insieme" [Definition and analytical expression of the perimeter of a set], Atti della Accademia Nazionale dei Lincei, Rendiconti della Classe di Scienze Fisiche, Matematiche e Naturali, 8 (in Italian), 14: 390–393, MR 0056066, Zbl 0051.29403. The first note published by De Giorgi on his approach to Caccioppoli sets.
  • De Giorgi, Ennio (1954), "Su una teoria generale della misura (r-1)-dimensionale in uno spazio ad r dimensioni" [On a general theory of (r - 1)-dimensional measure in r-dimensional space], Annali di Matematica Pura ed Applicata, IV (in Italian), 36 (1): 191–213, doi:10.1007/BF02412838, MR 0062214, Zbl 0055.28504. The first complete exposition of his approach to the theory of Caccioppoli sets by De Giorgi.
  • De Giorgi, Ennio; Ambrosio, Luigi (1988), "Un nuovo tipo di funzionale del calcolo delle variazioni" [A new kind of functional in the calculus of variations], Atti della Accademia Nazionale dei Lincei, Rendiconti della Classe di Scienze Fisiche, Matematiche e Naturali, 8 (in Italian and English), 82 (2): 199–210, MR 1152641, Zbl 0715.49014. The first paper on SBV functions and related variational problems.
  • Ambrosio, Luigi; De Giorgi, Ennio (1988), "Problemi di regolarità per un nuovo tipo di funzionale del calcolo delle variazioni" [Regularity problemsa for a new kind of functional in the calculus of variations], Atti della Accademia Nazionale dei Lincei, Rendiconti della Classe di Scienze Fisiche, Matematiche e Naturali, 8 (in Italian and English), 82 (4): 673–678, MR 1139814, Zbl 0735.49036.

Review papers

Books

  • De Giorgi, Ennio; Colombini, Ferruccio; Piccinini, Livio (1972), Frontiere orientate di misura minima e questioni collegate [Oriented boundaries of minimal measure and related questions], Quaderni (in Italian), Pisa: Edizioni della Normale, p. 180, MR 0493669, Zbl 0296.49031. An advanced text, oriented to the theory of minimal surfaces in the multi-dimensional setting, written by some of the leading contributors to the theory.
  • De Giorgi, Ennio (2006), Ambrosio, Luigi; Dal Maso, Gianni; Forti, Marco; Miranda, Mario; Spagnolo, Sergio, eds., Selected papers, Berlin–Heidelberg–New York: Springer-Verlag, doi:10.1007/978-3-642-41496-1, ISBN 978-3-540-26169-8, MR 2229237, Zbl 1096.01015 A selection from De Giorgi's scientific works, offered in an amended typographical form, in the original Italian language and English translation, including a biography, a bibliography and commentaries from Luis Caffarelli and other noted mathematicians.

See also

Notes

  1. ^ Piero D'Ancona (mathoverflow.net/users/7294), Should one attack hard problems?, http://mathoverflow.net/questions/124210 (version: 2013-03-11)

References

Biographical and general references

Scientific references

External links

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