Ennio de Giorgi

Ennio De Giorgi
Born	8 February 1928 Lecce, Italy
Died	25 October 1996 (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, 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

• De Giorgi, Ennio (1953), "Definizione ed espressione analitica del perimetro di un insieme", 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. "Definition and analytical expression of the perimeter of a set" is 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", Annali di Matematica Pura ed Applicata, IV (in Italian) 36 (1): 191–213, doi:10.1007/BF02412838, MR 0062214, Zbl 0055.28504. "On a general theory of (r - 1)-dimensional measure in r-dimensional space" is the first complete exposition by De Giorgi of the theory of Caccioppoli sets according to his.
• De Giorgi, Ennio; Colombini, Ferruccio; Piccinini, Livio (1972), Frontiere orientate di misura minima e questioni collegate, Quaderni (in Italian), Pisa: Edizioni della Normale, p. 180, MR 493669, Zbl 0296.49031. "Oriented boundaries of minimal measure and related questions" (English translation of the title) is 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.
• Ambrosio, Luigi; De Giorgi, Ennio (1988), "Un nuovo tipo di funzionale del calcolo delle variazioni", Atti della Accademia Nazionale dei Lincei, Rendiconti della Classe di Scienze Fisiche, Matematiche e Naturali, 8 (in Italian) 82 (2): 199–210, MR 1152641, Zbl 0715.49014 (with English summary). "A new kind of functional in the calculus of variations" (English translation of the title) is the first paper about SBV functions and related variational problems.
• De Giorgi, Ennio (1992), "Problemi variazionali con discontinuità libere", in Amaldi, E.; Amerio, L.; Fichera, G.; Gregory, T.; Grioli, G.; Martinelli, E.; Montalenti, G.; Pignedoli, A.; Salvini, Giorgio; Scorza Dragoni, Giuseppe, Convegno internazionale in memoria di Vito Volterra (8–11 ottobre 1990), Atti dei Convegni Lincei (in Italian) 92, Roma: Accademia Nazionale dei Lincei, pp. 39–76, ISSN 0391-805X, MR 1783032, Zbl 1039.49507. "Free-discontinuity variational problems" (English translation of the title) is a survey paper on free-discontinuity variational problems including several details on the theory of SBV functions, their applications and a rich bibliography (in Italian).
• De Giorgi, Ennio (2006), Ambrosio, Luigi; Dal Maso, Gianni; Forti, Marco; Miranda, Mario; Spagnolo, Sergio, eds., Selected papers, 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, 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

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

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

• 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 21 May 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 External link in |publisher= (help) 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" (PDF), 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.
• Faedo, Sandro (1997), "Come Ennio De Giorgi giunse alla Scuola Normale Superiore", Annali della Scuola Normale Superiore di Pisa. Classe di Scienze, Serie 4 (in Italian) 11 (3–4): 433–434, MR 1655526, Zbl 1001.01502. "How Ennio De Giorgi came to the Scuola Normale Superiore" is a brief commemorative historical describing the events which led Ennio De Giorgi to held a chair at the Scuola Normale Superiore.
• Lions, Jacques-Louis; Murat, François (October 1997), "Ennio De Giorgi (1928—1996)" (PDF), Notices of the AMS 44 (9): 1095–1096, MR 1470168, Zbl 0908.01025

Scientific 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 21 May 2011: web page of the scientific institution named after him at the Scuola Normale Superiore in Pisa.
• De Giorgi, Ennio (2001), Homepage, retrieved 21 May 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 21 May 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, 30 November 2006, retrieved 21 May 2011.
• Workshop "The Mathematics of Ennio De Giorgi, Pisa: Scuola Normale Superiore, 24–27 October 2001, retrieved 21 May 2011.