Renato Caccioppoli

Renato Caccioppoli (1904 to 1959) was an Italian mathematician known for his contributions to mathematical analysis, including functional analysis, the theory of measure and the study of differential equations. Born in Naples, he took his degree at the University of Naples in 1925, studying under Ernesto Pascal while being strongly influenced by Mauro Picone, whose assistant he became. He held the chair of algebraic analysis at Padua from 1931 before returning to Naples in 1934. His early work extended functionals beyond their initial domains and defined the area of curved surfaces, an approach later developed by Ennio de Giorgi, and the finite perimeter sets he introduced are now called Caccioppoli sets. From 1930 he applied topological and functional methods to existence problems for differential equations, proved the analyticity of C2 solutions of analytic elliptic equations in 1935, and later introduced pseudoanalytic functions. An open opponent of fascism, he was confined to an asylum in 1938 and resumed his scientific work after the war.