Gaetano Fichera (8 February 1922 – 1 June 1996) was an Italian mathematician, working in mathematical analysis, linear elasticity, partial differential equations and several complex variables.

He was immediately appointed by Picone as an assistant professor to his chair and as a researcher at the Istituto Nazionale per le Applicazioni del Calcolo, becoming his pupil.

Signorini had a strong long-time friendship with Picone: on a wall of the apartment building where they lived, in Via delle Tre Madonne, 18 in Rome, a memorial tablet which commemorates the two friends is placed, as Fichera (1995b, p. 47) recalls.

The two great mathematicians extended their friendship to the young Fichera, and as a consequence this led to the solution of the Signorini problem and the foundation of the theory of variational inequalities.

During a course on the theory of analytic functions of several complex variables taught at the Istituto Nazionale di Alta Matematica from the fall of 1956 and the beginning of the 1957, whose lectures were collected in the book (Severi 1958), Severi posed the problem of generalizing his theorem on the Dirichlet problem for holomorphic function of several variables, as Fichera (1957, p. 707) recalls: the result was the paper (Fichera 1957), which is a masterpiece, although not generally acknowledged for various reasons described by Range (2002, pp. 6–11).

Other scientists he had as teachers during the period 1939–1941 were Enrico Bompiani, Leonida Tonelli and Giuseppe Armellini: he remembered them with great respect and admiration, even if he did not share all their opinions and ideas, as Colautti Fichera (2006, p. 16) recalls.

A complete list of Fichera's friends includes some of the best scientists and mathematicians of the 20th century: Olga Oleinik, Olga Ladyzhenskaya, Israel Gel'fand, Ivan Petrovsky, Vladimir Maz'ya, Nikoloz Muskhelishvili, Ilia Vekua, Richard Courant, Fritz John, Kurt Friedrichs, Peter Lax, Louis Nirenberg, Ronald Rivlin, Hans Lewy, Clifford Truesdell, Edmund Hlawka, Ian Sneddon, Jean Leray, Alexander Weinstein, Alexander Ostrowski, Renato Caccioppoli, Solomon Mikhlin, Paul Naghdi, Marston Morse were among his friends, scientific collaborators and correspondents, just to name a few.

This long series of scientific journeys started in 1951, when he went to the USA together with his master and friend Mauro Picone and Bruno de Finetti in order to examine the capabilities and characteristics of the first electronic computers and purchase one for the Istituto Nazionale per le Applicazioni del Calcolo: the machine they advised to purchase was the first computer ever working in Italy.

Angelo, which was a student of mathematics at the University of Bologna under Gianfranco Cimmino, a former pupil of Mauro Picone, was charged of the task of testing the truth of Gaetano's assertions, examining him in mathematics: his question was:– "Mi sai dire una condizione sufficiente per scambiare un limite con un integrale (Can you give me a sufficient condition for interchanging limit and integration)?"–.

Gaetano quickly answered:– "Non solo ti darò la condizione sufficiente, ma ti darò anche la condizione necessaria e pure per insiemi non-limitati (I can give you not only a sufficient condition, but also a necessary condition, and not only for bounded domains, but also for unbounded domains)"–.

He is the author of more than 250 papers and 18 books (monographs and course notes): his work concerns mainly the fields of pure and applied mathematics listed below.

The work on this last topic started with the paper (Fichera 1963), where he announced the existence and uniqueness theorem for the Signorini problem, and ended with the following one (Fichera 1964a),[6] where the full proof was published: those papers are the founding works of the field of variational inequalities, as remarked by Stuart Antman in (Antman 1983, pp. 282–284).

Also he is known for his researches in the theory of hereditary elasticity: the paper (Fichera 1979b) emphasizes the necessity of analyzing very well the constitutive equations of materials with memory in order to introduce models where an existence and uniqueness theorems can be proved in such a way that the proof does not rely on an implicit choice of the topology of the function space where the problem is studied.

[9] His contributions to the calculus of variation are mainly devoted to the proof of existence and uniqueness theorems for maxima and minima of functionals of particular form, in conjunction with his studies on variational inequalities and linear elasticity in theoretical and applied problems: in the paper (Fichera 1964a) a semicontinuity theorem for a functional introduced in the same paper is proved in order to solve the Signorini problem, and this theorem was extended in (Fichera 1964c) to the case where the given functional has general linear operators as arguments, not necessarily partial differential operators.

Another branch of his studies on approximation theory is strictly tied to complex analysis in one variable, and to the already cited Mergelyan's theorem: he studied the problem of approximating continuous functions on a compact set (and analytic on its interior if this is non-void) of the complex plane by rational functions with prescribed poles, simple or not.

The paper (Fichera 1974b) surveys the contribution to the solution of this and related problems by Sergey Mergelyan, Lennart Carleson, Gábor Szegő as well as others, including his own.

In the first one he proves that a condition on a sequence of integrable functions previously introduced by Mauro Picone is both necessary and sufficient in order to assure that limit process and the integration process commute, both in bounded and unbounded domains: the theorem is similar in spirit to the dominated convergence theorem, which however only states a sufficient condition.

[14] Precisely, in the paper (Fichera 1957) he solved the Dirichlet problem for holomorphic function of several variables under the hypothesis that the boundary of the domain ∂Ω has a Hölder continuous normal vector (i.e. it belongs to the C{1,α} class) and the Dirichlet boundary condition is a function belonging to the Sobolev space H1/2(∂Ω) satisfying the weak form of the tangential Cauchy–Riemann condition,[15][16] extending a previous result of Francesco Severi: this theorem and the Lewy–Kneser theorem on the local Cauchy problem for holomorphic functions of several variables, laid the foundations of the theory of CR-functions.

[17] His contributions to the theory of exterior differential forms started as a war story:[18] having read a famous memoir of Enrico Betti (where Betti numbers were introduced) just before joining the army, he used this knowledge in order to develop a theory of exterior differential forms while he was kept prisoner in Teramo jail.

[19] When he was back in Rome in 1945, he discussed his discovery with Enzo Martinelli, who very tactfully informed him that the idea was already developed by mathematicians Élie Cartan and Georges de Rham.

He wrote bibliographical sketches for a number of mathematicians, both teachers, friends and collaborators, including Mauro Picone, Luigi Fantappiè, Pia Nalli, Maria Adelaide Sneider, Renato Caccioppoli, Solomon Mikhlin, Francesco Tricomi, Alexander Weinstein, Aldo Ghizzetti.