Ennio de Giorgi

Ennio De Giorgi
Born	(1928-02-08)February 8, 1928 Lecce, Italy
Died	October 25, 1996(1996-10-25) (aged 68) Pisa, Italy
Nationality	Italian
Fields	Calculus of variations, Partial differential equations
Institutions	University of Pisa
Alma mater	Sapienza University of Rome
Doctoral advisor	Mauro Picone
Known for	theory of Caccioppoli sets, solution of 19th Hilbert problem, existence and regularity theorem for minimal surfaces
Notable awards	Caccioppoli Prize (1960) Wolf Prize (1990)

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

Mathematical work

He solved Bernstein's problem about minimal surfaces.

He solved 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"

Selected publications

• Ambrosio, Luigi; De Giorgi, Ennio (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, with English summary) 82 (2): 199–210, MR 1152641, Zbl 0715.49014 . The first paper about SBV functions and related variational problems.
• 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 describing 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 e Applicata, IV (in Italian) 36 (1): 191–213, doi:10.1007/BF02412838, MR 0062214, Zbl 0055.28504 . The first complete exposition by De Giorgi of the theory of Caccioppoli sets.
• 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 493669, Zbl 0296.49031 . An advanced text, oriented to the theory of minimal surfaces in the multi-dimensional setting, written by one of the leading contributors.
• De Giorgi, Ennio (2006), Ambrosio, Luigi; Dal Maso, Gianni; Forti, Marco; Miranda, Mario; Spagnolo, Sergio, eds., Selected papers (in English and Italian), Berlin–Heidelberg–New York: Springer-Verlag, ISBN 978-3-540-26169-8, MR 2229237, Zbl 1096.01015  A selection from De Giorgi's scientific works with biography, bibliography and commentaries from Luis Caffarelli and other noted mathematicians.

See also

• Caccioppoli set
• Calculus of variations
• Elliptic partial differential equation
• Minimal surface

Biographical references

• Ambrosio, L.; Dal Maso, G.; Forti, M.; Miranda, M. (1999), "Ennio De Giorgi", Bollettino della Unione Matematica Italiana, Serie 8 (in Italian), Vol. 2-B (1): 3–31, MR 1794553, Zbl 0924.01022 . There is also a preprint version of this paper in Adobe pdf format, available at the web page of the Research Group in Calculus of Variations and Geometric Measure Theory, Scuola Normale Superiore, Pisa.
• Scuola Normale Superiore (2000), Biography of Ennio de Giorgi, retrieved May 21, 2011 , available home page at the Research Group in Calculus of Variations and Geometric Measure Theory, Scuola Normale Superiore, Pisa. A brief biography reviewing his major scientific contributions.
• De Cecco, Giuseppe; Rosato, Maria Letizia, eds. (2000), Ennio De Giorgi. Hanno detto di lui..., Quaderni del Dipartimento di Matematica dell' Università del Salento 5, Lecce: Coordinamento SIBA dell'Università di Lecce, p. 195, ISBN 88-8305-019-3  e-ISBN 88-8305-020-7. A collection of almost all commemorative papers, transcriptions of commemorative addresses on Ennio De Giorgi and personal reminiscences of pupils and friends, collected jointly with some philosophical papers of De Giorgi himself: the translation of the title reads as:"Ennio De Giorgi: they have said of him...".
• Emmer, Michele (October 1997), "Interview with Ennio De Giorgi", Notices of the AMS 44 (9): 1096–1101, MR 1470169, Zbl 0908.01026 .
• Emmer, Michele, ed. (2007), Mathematics and Culture IV, Berlin-Heidelberg-New York: Springer-Verlag, pp. viii+253, ISBN 978-3-540-34254-0, MR 2265420, Zbl 1127.00003 . Contains two chapters on De Giorgi.
• Lions, Jacques-Louis; Murat, François (October 1997), "Ennio De Giorgi (1928—1996)", Notices of the AMS 44 (9): 1095–1096, MR 1470168, Zbl 0908.01025 

References

• Giusti, Enrico (1984), Minimal surfaces and functions of bounded variations, Monographs in Mathematics 80, Basel-Boston-Stuttgart: Birkhäuser Verlag, pp. xii+240, ISBN 0-8176-3153-4, MR 0775682, Zbl 0545.49018 . An important monograph detailing the results of Ennio De Giorgi and his school on the Minimal surface problem approached by the theory of Caccioppoli sets.

External links

• Centro di ricerca matematica "Ennio de Giorgi", 2001, retrieved May 21, 2011 : web page of the scientific institution named after him at the Scuola Normale Superiore in Pisa.
• De Giorgi, Ennio (2001), Homepage, retrieved May 21, 2011  available at the web site of the Research Group in Calculus of Variations and Geometric Measure Theory, Scuola Normale Superiore, Pisa.
• Ennio De Giorgi at the Mathematics Genealogy Project
• Emmer, Michele (July 1996), Ennio De Giorgi (in Italian), retrieved May 21, 2011 . A video interview with its Italian transcription by Antonio Bernardo, available at Matematicamente thanks to the kind permission of Michele Emmer, of De Giorgi's family and of the Unione Matematica Italiana.
• O'Connor, John J.; Robertson, Edmund F., "Ennio de Giorgi", MacTutor History of Mathematics archive, University of St Andrews .
• Giornata in ricordo di Ennio De Giorgi (Meeting Day in memory of Ennio De Giorgi) (in Italian), Dipartimento di Matematica L. Tonelli, Faedo Hall,: Università di Pisa, November 30, 2006, retrieved May 21, 2011 .
• Workshop "The Mathematics of Ennio De Giorgi, Pisa: Scuola Normale Superiore, October 24–27, 2001, retrieved May 21, 2011 .