Ennio de Giorgi

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Ennio De Giorgi
Ennio de Giorgi.jpg
Born(1928-02-08)8 February 1928
Died25 October 1996(1996-10-25) (aged 68)
NationalityItalian
Alma materSapienza University of Rome
Known fortheory of Caccioppoli sets, solution of 19th Hilbert problem, existence and regularity theorem for minimal surfaces
Awards
Scientific career
FieldsCalculus of variations, Partial differential equations
InstitutionsScuola Normale Superiore di Pisa
Doctoral advisorMauro 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[edit]

He solved Bernstein's problem about minimal surfaces. Such surfaces arise as surfaces of smallest area spanning a given boundary. The proof required De Giorgi to develop his own version of what we now call geometric measure theory along with a related key compactness theorem. He was then able to conclude that a minimal hypersurface is analytic outside a closed subset of codimension at least two.

He solved the 19th Hilbert problem on the regularity of solutions of elliptic partial differential equations. At the time he began his studies, mathematicians were not able to handle anything beyond second order nonlinear elliptic equations in two variables. In his first major break-through in 1957, De Giorgi proved that solutions of uniformly elliptic second order equations of divergence form with only measurable coefficients were Hölder continuous. His results was proved in 1956/57 in parallel with John Nash, who was also working on the Hilbert problem. His results were the first among the two to be published, and it was anticipated that either mathematician would win the 1958 Fields Medal, but ultimately awarded to René Thom.

This work earned him lasting fame in the mathematical community, and was awarded many honours including the Caccioppoli Prize in 1960, the National Prize of Accademia dei Lincei from the President of the Italian Republic in 1973, and the Wolf Prize from the President of the Israel Republic in 1990. He was also awarded Honoris Causa degrees in Mathematics from the University of Paris in 1983 at a ceremony at the Sorbonne and in Philosophy from the University of Lecce in 1992. He was elected to many academies including: the Accademia dei Lincei, the Pontifical Academy of Sciences, the Academy of Sciences of Turin, the Lombard Institute of Science and Letters, the Académie des Sciences in Paris, and the National Academy of Sciences of the United States.

He was associated with may years the Scuola Normale Superiore in Pisa, leading a brilliant school of analysis in Europe at that time. He corresponded with many leading mathematicians of his time, such as Louis Nirenberg, John Nash and Renato Cacciopoli.

Quotes[edit]

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

Selected publications[edit]

Articles[edit]

Scientific papers[edit]

  • 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, hdl:10338.dmlcz/126043, 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[edit]

Books[edit]

  • 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, Springer Collected Works in Mathematics, 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[edit]

Notes[edit]

  1. ^ D'Ancona, Piero (March 11, 2013). "Should one attack hard problems?".

References[edit]

Biographical and general references[edit]

Scientific references[edit]

External links[edit]