Italian mathematician (1922–1996)
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 born in Acireale, and died in Rome.
Biography.
He was born in Acireale, a town near Catania in Sicily, the elder of the four sons of Giuseppe Fichera and Marianna Abate. His father Giuseppe was a professor of mathematics and influenced the young Gaetano starting his lifelong passion. In his young years he was a talented football player. On 1 February 1943 he was in the Italian Army and during the events of September 1943 he was taken prisoner by the Nazist troops, kept imprisoned in Teramo and then sent to Verona: he succeeded in escaping from there and reached the Italian region of Emilia-Romagna, spending with partisans the last year of war. After the war he was first in Rome and then in Trieste, where he met Matelda Colautti, who became his wife in 1952.
Education and academic career.
After graduating from the liceo classico in only two years, he entered the University of Catania at the age of 16, being there from 1937 to 1939 and studying under Pia Nalli. Then he went to the university of Rome, where in 1941 he earned his laurea with magna cum laude under the direction of Mauro Picone, when he was only 19. 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. After the war he went back to Rome working with Mauro Picone: in 1948 he became "Libero Docente" (free professor) of mathematical analysis and in 1949 he was appointed as full professor at the University of Trieste. As he remembers in , in both cases one of the members of the judging commission was Renato Caccioppoli, which become a close friend of him. From 1956 onward he was full professor at the University of Rome in the chair of mathematical analysis and then at the Istituto Nazionale di Alta Matematica in the chair of higher analysis, succeeding to Luigi Fantappiè. He retired from university teaching in 1992, but was professionally very active until his death in 1996: particularly, as a member of the Accademia Nazionale dei Lincei and first director of the journal "Rendiconti Lincei – Matematica e Applicazioni", he succeeded in reviving its reputation.
Honours.
He was member of several academies, notably of the Accademia Nazionale dei Lincei, the Accademia Nazionale delle Scienze detta dei XL and of the Russian Academy of Science.
Teachers.
His lifelong friendship with his teacher Mauro Picone is remembered by him in several occasions. As recalled by , his father Giuseppe was an assistant professor to the chair of Picone while he was teaching at the University of Catania: they become friends and their friendship lasted even when Giuseppe was forced to leave the academic career for economic reasons, being already the father of two sons, until Giuseppe's death. The young, in effect child, Gaetano, was kept by Picone in his arms. From 1939 to 1941 the young Fichera developed his research directly under the supervision of Picone: as he remembers, it was a time of intense work. But also, when he was back from the front in April 1945 he met Picone while he was in Roma in his way back to Sicily, and his advisor was so happy to see him as a father can be seeing its living child. Another mathematician Fichera was influenced by and acknowledged as one of his teachers and inspirators was Pia Nalli: she was an outstanding analyst, teaching for several years at the University of Catania, being his teacher of mathematical analysis from 1937 to 1939. Antonio Signorini and Francesco Severi were two of Fichera's teachers of the Roman period: the first one introduced him and inspired his research in the field of linear elasticity while the second inspired his research in the field he taught him i.e. the theory of analytic functions of several complex variables. 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 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. Fichera's relations with Severi were not as friendly as with Signorini and Picone: nevertheless, Severi, which was one of the most influential Italian mathematicians of the first half of the 20th century, esteemed the young mathematician. 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 posed the problem of generalizing his theorem on the Dirichlet problem for holomorphic function of several variables, as recalls: the result was the paper , which is a masterpiece, although not generally acknowledged for various reasons described by . 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 recalls.
Friends.
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. He built up such a network of contacts being invited several times to lecture on his research by various universities and research institutions, and also participating to several academic conferences, always upon invitation. 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. The most complete source about his friends and collaborators is the book by his wife Matelda: in those reference it is also possible to find a fairly complete description of Gaetano Fichera's scientific journeys.
The close friendship between Angelo Pescarini and Fichera has not his roots in their scientific interests: it is another war story. As recalls, Gaetano, being escaped from Verona and hidden in a convent in Alfonsine, tried to get in touch with the local group of partisans in order to help the people of that town who had been so helpful with him: they were informed about an assistant professor to the chair of higher analysis in Rome who was trying to reach them. 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)"–. In effect, Fichera proved such a theorem in the paper , his latest paper written in while he was in Rome before joining the army: from that moment on he often used to joke saying that good mathematicians can always have a good application, even for saving one's life.
One of his best friends and appreciated scientific collaborator was Olga Arsenievna Oleinik: she cured the redaction of his last posthumous paper , as recalls. Also, she used to discuss his work with Gaetano, as he did with her: sometimes their discussion become lively, but nothing more, since they were extremely good friends and estimators of each one's work.
Work.
Research activity.
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. A common characteristic to all of his research is the use of the methods of functional analysis to prove existence, uniqueness and approximation theorems for the various problems he studied, and also a high consideration of the analytic problems related to problems in applied mathematics.
Mathematical theory of elasticity.
His work in elasticity theory includes the paper , where Fichera proves the "Fichera's maximum principle", his work on variational inequalities. The work on this last topic started with the paper , where he announced the existence and uniqueness theorem for the Signorini problem, and ended with the following one , where the full proof was published: those papers are the founding works of the field of variational inequalities, as remarked by Stuart Antman in . Concerning the Saint-Venant's principle, he was able to prove it using a variational approach and a slight variation of a technique employed by Richard Toupin to study the same problem: in the paper there is a complete proof of the principle under the hypothesis that the base of the cylinder is a set with piecewise smooth boundary. Also he is known for his researches in the theory of hereditary elasticity: the paper 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. At last, it is worth to mention that Clifford Truesdell invited him to write the contributions and for Siegfried Flügge's "Handbuch der Physik".
Partial differential equations.
He was one of the pioneers in the development of the abstract approach through functional analysis in order to study general boundary value problems for linear partial differential equations proving in the paper a theorem similar in spirit to the Lax–Milgram theorem. He studied deeply the mixed boundary value problem i.e. a boundary value problem where the boundary has to satisfy a mixed boundary condition: in his first paper on the topic, , he proves the first existence theorem for the mixed boundary problem for self-adjoint operators of "n"  ; 2 variables, while in the paper he proves the same theorem dropping the hypothesis of self-adjointness. He is, according to , the founder of the theory of partial differential equations of non-positive characteristics: in the paper he introduced the now called Fichera's function, in order to identify subsets of the boundary of the domain where the boundary value problem for such kind of equations is posed, where it is necessary or not to specify the boundary condition: another account of the theory can be found in the paper , which is written in English and was later translated in Russian and Hungarian.
Calculus of variation.
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 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 to the case where the given functional has general linear operators as arguments, not necessarily partial differential operators.
Functional analysis and eigenvalue theory.
It is difficult to single out his contributions to functional analysis since, as stated at the beginning of this section, the methods of functional analysis are ubiquitous in his research: however, it is worth to remember paper , where an important existence theorem is proved.
His contributions in the field