Enrico Giusti is an Italian mathematician mainly known for his contributions to the fields of calculus of variations

Calculus of variations

Calculus of variations is a field of mathematics that deals with extremizing functionals, as opposed to ordinary calculus which deals with functions. A functional is usually a mapping from a set of functions to the real numbers. Functionals are often formed as definite integrals involving unknown...

, regularity theory of partial differential equation

Partial differential equation

In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...

s, minimal surfaces and history of mathematics

History of mathematics

The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past....

. He has been professor of mathematics at the Università di Firenze

University of Florence

The University of Florence is a higher study institute in Florence, central Italy. One of the largest and oldest universities in the country, it consists of 12 faculties...

; he also taught and conducted research at the Australian National University

Australian National University

The Australian National University is a teaching and research university located in the Australian capital, Canberra.As of 2009, the ANU employs 3,945 administrative staff who teach approximately 10,000 undergraduates, and 7,500 postgraduate students...

 at Canberra, at the Stanford University

Stanford University

The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is a private research university on an campus located near Palo Alto, California. It is situated in the northwestern Santa Clara Valley on the San Francisco Peninsula, approximately northwest of San...

 and at the University of California, Berkeley

University of California, Berkeley

The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...

. After retirement, he devoted himself to the managing of the "Giardino di Archimede", a museum entirely dedicated to mathematics and its applications. Giusti is also the editor-in-chief of the international journal, dedicated to the history of mathematics "Bollettino di storia delle scienze matematiche".

One of the most famous results of Giusti, is the one obtained with Enrico Bombieri

Enrico Bombieri

Enrico Bombieri is a mathematician who has been working at the Institute for Advanced Study in Princeton, New Jersey. Bombieri's research in number theory, algebraic geometry, and mathematical analysis have earned him many international prizes --- a Fields Medal in 1974 and the Balzan Prize in 1980...

 and Ennio De Giorgi

Ennio de Giorgi

-References:. The first paper about SBV functions and related variational problems.. The first note published by De Giorgi describing his approach to Caccioppoli sets.. The first complete exposition by De Giorgi of the theory of Caccioppoli sets.. An advanced text, oriented to the theory of minimal...

, concerning the minimality of Simons

James Harris Simons

James Harris "Jim" Simons is an American hedge fund manager, mathematician, and philanthropist.In 1982, Simons founded Renaissance Technologies, a private investment firm based in New York with over $15 billion under management; Simons is still at the helm, as CEO, of what is now one of the...

' cones, and allowing to disprove the validity of Bernstein's theorem

Bernstein's problem

In differential geometry, Bernstein's problem is as follows: if the graph of a function on Rn−1 is a minimal surface in Rn, does this imply that the function is linear?...

 in dimension larger than 8. The work on minimal surfaces was mentioned in the citation of the Fields medal

Fields Medal

The Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union , a meeting that takes place every four...

 eventually awarded to Bombieri in 1974.

Awards

Giusti won the Caccioppoli Prize

Caccioppoli Prize

The Caccioppoli Prize is awarded by the Italian Mathematical Union to an Italian mathematician not exceeding the age of 38 who established a wide international reputation . The prize is entitled to the memory of the Italian mathematician Renato Caccioppoli and is awarded on the occasion of the...

 of the Italian Mathematical Union

Italian Mathematical Union

The Italian Mathematical Union is a mathematics society based in Italy. It was founded on December 7, 1922 by Luigi Bianchi, Vito Volterra, and most notably, Salvatore Pincherle, who became the Union's first President...

 in 1978 and in 2003 was awarded with the national medal for mathematics by the Accademia Nazionale delle Scienze (dei XL).

Selected publications

• "Minimal cones and the Bernstein problem" (with E. Bombieri e E. De Giorgi), Inventiones Mathematicae 7 (1969) 243–268
• "Harnack's inequality
  Harnack's inequality
  In mathematics, Harnack's inequality is an inequality relating the values of a positive harmonic function at two points, introduced by . and generalized Harnack's inequality to solutions of elliptic or parabolic partial differential equations. Perelman's solution of the Poincaré conjecture uses...
  
  for elliptic differential equations on minimal surfaces" (with E. Bombieri), Inventiones Mathematicae 15 (1972), 24–46
• "On the equation of surfaces of prescribed mean curvature. Existence and uniqueness without boundary conditions", Inventiones Mathematicae 46 (1978), 111–137
• "On the regularity of the minima of variational integrals" (with M. Giaquinta), Acta Mathematica 148 (1982), 31–46
• "Differentiability of minima of nondifferentiable functionals" (with M. Giaquinta), Inventiones Mathematicae 72 (1983), 285–298
• "The singular set of the minima of certain quadratic functionals" (with M. Giaquinta), Annali della Scuola Normale Superiore di Pisa Classe di Scienze (Serie 4) 11 (1984), 45–55
• "Minimal surfaces and functions of bounded variation", Monographs in Mathematics, 80. Birkhäuser Verlag, Basel, 1984. ISBN 0-8176-3153-4
• "Direct methods in the calculus of variations", World Scientific Publishing Co., Inc., River Edge, NJ, 2003. ISBN 981-238-043-4