Selected Papers

The book contains a selection of 43 scientific papers by the great mathematician Ennio De Giorgi (1928-1996), which display the broad range of his achievements and his entire intellectual career as a problem solver and as a proponent of deep and ambitious mathematical theories. All papers are written in English and 17 of them appear also in their original Italian version in order to give an impression of De Giorgi’s original style. The editors also provide a short biography of Ennio De Giorgi and a detailed account of his scientific achievements, ranging from his seminal paper on the solution of Hilbert’s 19th problem to the theory of perimeter and minimal surfaces, the theory of G-convergence and the foundations of mathematics.

• Calculus of variations
• Foundations of mathematics
• G-convergence
• MSC (2000): 03-99, 35-99, 35B65, 49J45, 49Q05, 49Q15, 49Q20
• Minimal surfaces
• Partial differential equations

From the reviews:

"The book under review is a collection of selected papers by Ennio De Giorgi (1928-1996). … The book has been very carefully prepared and printed. It is a valuable source for all interested in the work of De Giorgi. It presents the broad range of his achievements and his entire intellectual path, as a problem solver and as a proponent of deep and ambitious mathematical theories." (Roman Murawski, Zentrablatt MATH, Vol. 1096 (22), 2006)

"This volume contains a well-balanced choice of papers written by Ennio De Giorgi, an outstanding Italian mathematician of the 20th century. … In my opinion the volume, which covers all the main directions of the author’s activities (measure theory, the 19th Hilbert problem, minimal hypersurfaces, G- and D-convergence, and foundations of mathematics) should be on the shelves of every mathematical library." (EMS Newsletter, December 2006)

• Napoli, Italy

  Luigi Ambrosio

• SISSA, Trieste, Italy

  Gianni Dal Maso

• Università di Pisa Dipto. Matematica Applicata, Pisa, Italy

  Marco Forti

• Centro Internationale per la Ricerca Matematica, Trento, Italy

  Mario Miranda

• University of Pisa, Pisa, Italy

  Sergio Spagnolo, Ennio De Giorgi

Ennio de Giorgi (Lecce, February 8, 1928 – Pisa, October 25, 1996) was an influential 20th century Italian mathematician. He made important contributions to mathematical analysis, in particular to the study of minimal surfaces and to the regularity of the solutions of elliptic partial differential equations. One of his major contributions to the latter was to solve the 19th Hilbert problem, which John Forbes Nash solved independently at roughly the same time. His work has influenced Luis Caffarelli and many other mathematicians.

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