[citation needed] This achievement not only brought Ennio immediate recognition but displayed his ability to attack problems using completely new and effective methods which, though conceived before, can be used with greater precision as shown in his research works.

In a major breakthrough, De Giorgi proved that solutions of uniformly elliptic second-order equations of divergence form, with only measurable coefficients, were Hölder continuous.

Nevertheless, De Giorgi's work opened up the field of nonlinear elliptic partial differential equations in higher dimensions which paved a new period for all of mathematical analysis.

Almost all of his work relates to partial differential equations, minimal surfaces and calculus of variations; these notify the early triumphs of the then-unestablished field of geometric analysis.

[citation needed] The work of Karen Uhlenbeck, Shing-Tung Yau and many others have taken inspiration from De Giorgi which have been and continue to be extended and rebuilt in powerful and effective mannerisms.

[citation needed] In 2016, a conference was held at the Scuola Normale in Pisa in memory of De Giorgi, and mathematicians like Camillo de Lellis, Irene Fonseca, Pierre-Louis Lions, Haïm Brezis, Alessio Figalli, David Kinderlehrer, Nicola Fusco, Felix Otto, Giuseppe Mingione and Louis Nirenberg have attended the event along with his many students such as Ambrosio and Braides who have been responsible for organizing it at the SNS.