Eugenio Elia Levi (18 October 1883 – 28 October 1917) was an Italian mathematician, known for his fundamental contributions in group theory, in the theory of partial differential operators and in the theory of functions of several complex variables. He was a younger brother of Beppo Levi and was killed in action during First World War.

Work

Research activity

He wrote 33 papers, classified by his colleague and friend Mauro Picone according to the scheme reproduced in this section.

Differential geometry

Group theory

He wrote only three papers in group theory: in the first one, discovered what is now called Levi decomposition, which was conjectured by Wilhelm Killing and proved by Élie Cartan in a special case.

Function theory

In the theory of functions of several complex variables he introduced the concept of pseudoconvexity during his investigations on the domain of existence of such functions: it turned out to be one of the key concepts of the theory.

Cauchy and Goursat problems

Boundary value problems

His researches in the theory of partial differential operators lead to the method of the parametrix, which is basically a way to construct fundamental solutions for elliptic partial differential operators with variable coefficients: the parametrix is widely used in the theory of pseudodifferential operators.

Calculus of variations

Publications

The full scientific production of Eugenio Elia Levi is collected in reference.

Biographical and general references