# Enrico Magenes

### Born: 15 April 1923 in Milan, Italy

Died: 2 November 2010 in Pavia, Italy

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**Enrico Magenes**entered the Scuola Normale Superiore in Pisa in 1938 where he studied mathematics. However, his studies were severely disrupted by the advent of World War II. Italy did not enter the war following the German invasion of Poland in September 1939. However, in June 1940, just before the fall of France, Italy entered the war on the German side. As a student, Magenes belonged to Azione Cattolica (Catholic Action) which was a non-political lay organization of Catholics. Political parties were prohibited under Mussolini's Fascist rule but the non-political nature of Catholic Action meant that it could continue to exist and it received strong support from the Vatican. Magenes had held a leading role in the local branch of Azione Cattolica in Pisa from 1938 to 1941. He continued with his studies until 1941 when he was forced to stop. He was in Pavia in July 1943 when the Allies invaded Italy and later that month Mussolini resigned and the Fascist party in Italy was dissolved. However, in Pavia life went on much as before with people still belonging to the old parties that had existed before the Fascist period, in particular the Italian People's Party. The Allies slowly fought their way north and in September 1943 Italy surrendered to the Allies and declared war on Germany in the following month.

In August 1943, Magenes was involved in trying to revive the Christian Democrats party in Pavia. A number of parties of very different political views, but all opposed to Fascism and German occupation of Italy, came together to form the Comitato di Liberazione Nazionale (Committee of National Liberation) on 9 September 1943. As well as the Christian Democrats, there were parties such as the Italian Communists, the Italian Liberals, Italian Republicans and the Italian Socialists. Magenes became a member of the Pavia branch of the Committee of National Liberation from its foundation, committed to fight the war of liberation alongside their Anglo-American allies. On 8 January 1944, Magenes and four other members of the Pavia branch of the Committee of National Liberation, were arrested by the Republican National Guard and put in prison in Pavia. They were interrogated but remained in Pavia until July when the SS took them to San Vittore where they were put in solitary confinement.

On 17 August they were taken to Bolzano, then taken by train to Flossenburg where they spent a month in quarantine. Two of the four men arrested in Pavia with Magenes died in Flossenburg. Magenes was then sent to work at Kottern, part of the Dachau concentration camp north of Munich, where he worked at the Messerschmitt airplane factory. In April 1945 allied troops reached the Kottern district and Magenes was sent Innsbruck. He managed to reach Switzerland where he was put into a camp for Italian prisoners. Magenes remained in Switzerland until July when he was able to go to Milan. As soon as it became possible, Magenes returned to Pisa to continue his studies at the Scuola Normale Superiore. Advised by Leonida Tonelli and Giovanni Sansone, he completed his laurea in mathematics in 1947. We should note that Tonelli, who was a professor at the University of Pisa, died in 1946 while Magenes was studying with him. Sansone had been a student at the Scuola Normale Superiore of Pisa and after being appointed professor of mathematics at various universities, was appointed to the Scuola Normale Superiore of Pisa when Magenes was nearing the end of his laurea studies. Sansone made important contributions to analysis, particularly with his studies of ordinary differential equations.

Magenes published the paper

*Sui teoremi di Tonelli per la semicontinuità nei problemi di Mayer e di Lagrange*Ⓣ in 1946, before submitting his laurea thesis. This paper gives a detailed proof of a theorem due to Tonelli. In 1947 he published a two-part paper

*Sopra un problema di T Satô per l'equazione differenziale*

*y*" =

*f*(

*x*,

*y*,

*y*') Ⓣ. The paper considers the problem of the existence of solutions of the differential equation in the title which pass through a given point and are tangent to a given curve. In 1948 he published two papers,

*Problemi di valori al contorno per l'equazione differenziale*

*y*

^{(n)}=

*λ*

*f*(

*x*,

*y*,

*y*', ... ,

*y*

^{(n-1)}) Ⓣ and

*Una questione di stabilità relativa ad un problema di moto centrale a massa variabile*Ⓣ. The first of these papers examines the values of

*λ*for which the equation in the title, subject to certain boundary conditions, has a solution. This is a nonlinear Sturm-Liouville problem. The second paper looks at properties of the motion of a particle in the gravitational field of a fixed massive particle. He wrote two papers on "Fubini-Tonelli'' integrals in 1948 but they were not published until 1950. These are

*Intorno agli integrali di Fubini-Tonelli. I. Condizioni sufficienti per la semicontinuità*Ⓣ; and

*Intorno agli integrali di Fubini-Tonelli. II. Teoremi di esistenza dell'estremo*Ⓣ.

Mathematical life in Italy slowly began to return to normal following the end of World War II. In September 1948 the Italian Mathematical Union held it Third Congress in Pisa, the first congress after World War II. Magenes attended the Congress and his views of this Congress is given in [5]. He writes:-

Magenes was appointed as an assistant at the University of Padua in 1948. He competed for professorships, and was appointed as a professor straordinario to the University of Modena in 1952 after being ranked first in the competition for the chair. Three years later, in 1955, he moved to a professorship at the University of Genoa. This time it was a position he held for four years before returning to the University of Pavia in 1959 when he was appointed to the chair of higher analysis. He founded the Institute for Numerical Analysis of the CNR (named the Istituto di Matematica Applicata e Tecnologie Informatiche (IMATI), and now named after Enrico Magenes) in 1970 and directed it for over 20 years. He also became president of the Collegio Universitario Santa Caterina da Siena, one of the four colleges of the University of Pavia. Virginio Rognoni said [6]:-What impressions did the Congress make on us, particularly given our expectations, even if these had not been clearly formed? I think they can essentially be summarised as follows: above all we had it confirmed that among Italian mathematicians, especially among the elder ones, there was quite a feeling of distrust towards the trend towards greater abstraction in mathematics cultivated abroad in the last years. This feeling was clear in the excellent and interesting speech given by Francesco Severi, and also in the lack of a section dedicated to algebra, while the tradition of the great Italian school of algebraic geometry was confirmed. But also in the field of Italian analysis, as we had already realised at the Scuola Normale Superiore, it was seen towards the theories of abstract spaces, born mainly in Poland with Stefan Banach and in France with Bourbaki.

He spent the rest of his career at Pavia, retiring in 1996 and, at that time, was made professor emeritus.Enrico Magenes was chosen by bishop Angioni to be president of the newly founded women's college Santa Caterina da Siena. The College had been proposed and so-named by pope Paul VI who, for many years, had realised the importance of building a home in Pavia to accommodate young women, university students, capable and worthy, as had been the case for centuries for male students. Enrico Magenes strove to lead the College for over thirty years with great generosity, even supporting it financially and trying to include it immediately into the great tradition of the historic colleges of Pavia. Through his actions Magenes was clear that his idea for the proper growth and development of talented students, through encouraging merit, must be accompanied by a climate of attention to people respecting and sharing with others, as in a large family open to the religious and moral requirements of the modern world. That is still the spirit of our College, when we are nearing forty years after its founding. That today Santa Caterina exists and is recognised as one of the fourteen leading Italian university colleges, we owe to Enrico Magenes.

Magenes's most important work was done in collaboration with the French mathematician Jacques-Louis Lions. He described in [3] how that work began:-

Together they investigated inhomogeneous boundary problems for elliptic equations and inhomogeneous initial-boundary value problems for parabolic and hyperbolic evolution equations. The work which they did in this area was included in their three volume treatise... in Nice in the summer of1957at the Réunion des Mathématiciens d'Expression Latine, ... Guido Stampacchia and I had the opportunity to meet Lions and to become friends with him because of common scientific interests and life experiences. Stampacchia and I wanted to know and make known in Italy the results of the school of Laurent Schwartz on distributions and on partial differential equations. At our invitation Lions came to Genoa in April1958to give a series of lectures on mixed problems in the sense of Hadamard ...

*Problèmes aux limites non homogènes et applications*Ⓣ. Volumes 1 and 2 were published in 1968 with the third volume appearing in 1970. R S Freeman, reviewing Volume 1 writes:-

Freeman also reviewed Volume 2 and Volume 3, writing in the review of the third volume:-This book was not written with the first year graduate student in mind: the authors use such topics as the Hille-Yosida theory of one-parameter semigroups, the spectral theorem in Hilbert space, portions of the theory of distributions, and several other topics. Also, in some cases the results are only outlined, though in most cases references are given. However, although the demands are great, the returns are in proportion: the problems treated are of fundamental importance and the results are penetrating and powerful. Moreover, and almost as important, the whole discussion is carried out with grace and elegance and is a striking example of the interplay between classical analysis and functional analysis. If there are still people who feel that the subject of partial differential equations is "dirty" mathematics, this work should refute them once and for all.

The Committee for International Conferences on Industrial and Applied Mathematics awarded Maqenes their Lagrange Prize in 2003. The citation reads as follows:-... whereas the first two volumes were concerned almost entirely with Hilbert spaces the present volume involves more general locally convex spaces. Another and perhaps more important difference is that the theory of the spaces in question is no longer presented in great detail: the authors content themselves with stating the results used, referring the reader to the literature for proofs. However, in the later chapters the methods used as well as the proofs of the most important results are presented in great detail; when proofs are not given they are outlined and are similar to earlier proofs. In general one would have to be hypercritical to find fault with the exposition. ... as in the first two volumes, the results are deep and penetrating and the exposition is masterful. It is a work to be recommended to every serious student of partial differential equations and particularly to those who are fascinated by the manner in which modern functional analysis has aided and influenced their study.

This was certainly not the only honour that Magenes received. He was elected to numerous academies including: the Accademia Nazionale dei Lincei, the Istituto Lombardo, the Accademia di Scienze e Lettere, the Société Royale des Sciences de Liege, and the Academia Europaea. He was president of the Italian Mathematical Union from 1973 to 1975. After his death, students, friends and colleagues organised the conference 'Analysis and Numerics of Partial Differential Equations' in his memory at Pavia in November 2011. Let us end this biography with the opening sentences of Alberto Farina's tribute to Magenes, delivered at the first Lions-Magenes Day in Paris on 14 December 2011:-The ICIAM Lagrange Prize for2003is awarded to Professor Enrico Magnes(Università di Pavia), for his contributions to the development of Applied Mathematics at the world-wide level. In a remarkable series of papers, followed and made complete in a three-volume book in cooperation with J L Lions(Nonhomogeneous Boundary Value Problems and Applications), he set the foundations for the modern treatment of partial differential equations, and in particular the ones mostly used in applications. This includes the systematic treatment of variational formulations, as well as the paradigm "regularity-results-transposition-interpolation," and allows a fully detailed use of the properties of trace spaces. The book has been the reference book for more than thirty years, for the completeness of the results reported there, but even more for the strategy of approach to problems. After that, the scientific activity of Magenes moved even further in the direction of application. In the early seventies he founded the Institute of Numerical Analysis in Pavia, which he directed for more than twenty years, keeping it in close contact with the top level scientific institutions all over the world, and making it the source of a number of highly successful scientists and of several pioneering results. Apart from his continuous inspirational influence, he contributed personally to the development of a totally new technique for treating free boundary problems by means of variational inequalities, with remarkable applications to several important problems such as the flow of fluids through porous media or the phase-change phenomena. But even if his own results have been of paramount importance, his major merit is surely in the impulse he gave, and the influence he had in starting, encouraging and sustaining a way of doing mathematics that joined the rigour, the elegance and the deepness of so-called pure mathematics with the real-life problems that have to be faced in applications. If the combination of pure mathematics and applications is what Applied Mathematics is nowadays, Magenes is surely among the ones that deserve most credit.

The contributions of Enrico Magenes to mathematics and its applications have been numerous and remarkable. Who has not trembled before the three volumes: 'Nonhomogeneous Boundary Value Problems and Applications', written in collaboration with Jacques-Louis Lions. Trembled with admiration at the depth, modernity and vision of a work which is so outstanding.

**Article by:** *J J O'Connor* and *E F Robertson*

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