Ennio De Giorgi
Wolf Prize Laureate in Mathematics 1990
Ennio De Giorgi
Affiliation at the time of the award:
Scuola Normale Superiore, Italy
Award citation:
“for his innovating ideas and fundamental achievements in partial differential equations and calculus of variations”.
Prize share:
Ennio De Giorgi
Ilya Piatetski-Shapiro
The work of Professor Ennio De Giorgi is among the most important and creative accomplishments in the theory of partial differential equations and the calculus of variations. 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 Holder continuous. Probably his greatest contribution cue in 1960; this was a regularity theory for minimal hypersurfaces. 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. Since then he and his school have settled litany of the outstanding problems in this area.
