Tommaso Boggio

Tommaso Boggio

Tommaso Boggio (born December 22, 1877 in Valperga , † May 25, 1963 in Turin ) was an Italian mathematician .

Life

Boggio grew up in Turin, received scholarships for school attendance because he came from a modest background and stood out for his talent, and studied mathematics at the University of Turin with a Laureate degree in 1899. He then worked as an assistant for projective and descriptive geometry in Turin with Mario Pieri , which he continued to teach when Pieri left Turin in 1900. In addition, the first publications in mathematical physics followed. From 1903 he taught mathematical physics at the University of Pavia and at the same time as an assistant to Giuseppe Peano Analysis in Turin. In 1905, after a competition, he became professor of financial mathematics at the higher commercial school in Genoa (later part of the University of Genoa). In 1908, after a competition, he won the chair of rational mechanics at the University of Messina . He survived the devastating earthquake in Messina that followed soon after and briefly taught in Florence.

Boggio was professor of higher mechanics in Turin from 1909 to 1947, succeeding Giacinto Morera . After Enrico D'Ovidio retired in 1918, he also taught algebraic analysis and analytical geometry there. He also taught at the Military Academy in Turin and Modena. He taught until 1950 after his retirement.

Boggio is buried in Axams next to his second son.

plant

He dealt with mechanics, differential geometry, mathematical physics, analysis and financial mathematics.

With Cesare Burali-Forti he developed a failed attempt at a coordinate-free formulation of the theory of curved spaces in differential geometry, which they published in a book in 1924 (Espaces courbes. Critique de la Relativité), which at the same time attacked the general theory of relativity. With Burali-Forti he also wrote a monograph on theoretical mechanics.

In contrast, his contributions are still important in potential theory today. He developed an explicit representation of Green's function as a solution to the polyharmonic Dirichlet problem in n-dimensions (Boggio's formula) and introduced Boggio's principle:

Let in the unit ball be in n dimensions with the Neumann boundary condition on the boundary, then is in the unit ball. ${\displaystyle {\Delta }^{2}u\geq 0}$ ${\displaystyle {\frac {\partial u}{\partial n}}=0}$ ${\displaystyle u\geq 0}$

Biharmonic functions appear in the theory of deformations and vibrations of elastic plates. The Boggio-Hadamard conjecture (Hadamard, Boggio, around 1908) is named after him and Jacques Hadamard . It says that the Green's functions of a thin elastic plate clamped at the sides are always positive (the membrane always moves in the direction of the load, no matter where the load is placed). Let D be in a convex, smooth, simply connected domain with Dirichlet and Neumann boundary conditions on the boundary of D, then it follows that . ${\displaystyle {\Delta }^{2}u=f}$ ${\displaystyle u=0,{\frac {\partial u}{\partial n}}=0}$ ${\displaystyle f\geq 0}$ ${\displaystyle u\geq 0}$

The conjecture was refuted by Richard Duffin in 1949 for smooth convex areas and many other counterexamples have been found since then.

Honors and memberships

In 1907 he received with Jacques Hadamard , Arthur Korn and Giuseppe Lauricella (1867-1913) the Prix Vaillant of the French Académie des Sciences, which was awarded after a prize on elastic plates and whose judge was Henri Poincaré . He became a member of the Institut de France. He was a Grand Officer of the Order of the Crown of Italy , Officer of the Order of St. Maurizio e Lazzaro and a member of the Accademia delle Scienze di Torino .

In 1908 he lectured at the International Congress of Mathematicians (ICM) in Rome (Sopra alcuni teoremi di fisica-matematica).

Web links

• John J. O'Connor, Edmund F. Robertson :  Tommaso Boggio. In: MacTutor History of Mathematics archive .
• Italian biography

Remarks

1. ↑ That is, as a solution to the mth power of the Laplace operator
2. ↑ Hadamard posed the problem in his lecture at the International Congress of Mathematicians in Rome in 1908. In the same year, his prize paper, the Mémoires of the French Academy, was published on the equilibrium of clamped elastic plates.

Individual evidence

1. ↑ George Rainich , Review in American Mathematical Monthly, Volume 33, 1926, pp. 515-517. They did not succeed in representing the Riemann curvature tensor in an invariant way, which is why they thought it was of no importance.
2. ^ Boggio, Burali-Forte, Meccanica razionale, 1921
3. ↑ Boggio, Sulle funzioni di Green d'ordine m, Rendiconti del Circolo Matematico di Palermo, Volume 20, 1905, pp. 97-135
4. ↑ Filippo Gazzola, Filippo, Hans-Christoph Grunau, Guido Sweers: Polyharmonic Boundary Value Problems, Lecture Notes in Mathematics 1991, Springer 2010, pdf
5. ↑ Michel Chipot (Ed.), Handbook of Differential Equations, Volume 6, Elsevier 2008, p. 159
6. ↑ Duffin, On a question of Hadamard concerning super-biharmonic functions, J. Math. Phys., Volume 27, 1949, pp. 253-258