Ennio de Giorgi
Encyclopedia
Ennio de Giorgi was an Italian mathematician who worked on 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 and the foundations of mathematics.

Mathematical work

He solved Bernstein's problem
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?...

 about minimal surface
Minimal surface
In mathematics, a minimal surface is a surface with a mean curvature of zero.These include, but are not limited to, surfaces of minimum area subject to various constraints....

s.

He solved 19th Hilbert problem
Hilbert's nineteenth problem
Hilbert's nineteenth problem is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. It asks whether the solutions of regular problems in the calculus of variations are always analytic.-History:...

 on the regularity of solutions of elliptic partial differential equations.

See also

  • Caccioppoli set
    Caccioppoli set
    In mathematics, a Caccioppoli set is a set whose boundary is measurable and has a finite measure. A synonym is set of finite perimeter...

  • 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...

  • Elliptic partial differential equation
  • Minimal surface
    Minimal surface
    In mathematics, a minimal surface is a surface with a mean curvature of zero.These include, but are not limited to, surfaces of minimum area subject to various constraints....


External links

: web page
Web page
A web page or webpage is a document or information resource that is suitable for the World Wide Web and can be accessed through a web browser and displayed on a monitor or mobile device. This information is usually in HTML or XHTML format, and may provide navigation to other web pages via hypertext...

 of the scientific institution named after him at the Scuola Normale Superiore in Pisa
Pisa
Pisa is a city in Tuscany, Central Italy, on the right bank of the mouth of the River Arno on the Tyrrhenian Sea. It is the capital city of the Province of Pisa...

. available at the web site of the Research Group in Calculus of Variations and Geometric Measure Theory, Scuola Normale Superiore, Pisa
Pisa
Pisa is a city in Tuscany, Central Italy, on the right bank of the mouth of the River Arno on the Tyrrhenian Sea. It is the capital city of the Province of Pisa...

.. 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...
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