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Person: Mikhlin, Solomon Grigoryevich

Solomon Grigoryevich Mikhlin was a Belarussian mathematician of who worked in the fields of linear elasticity, singular integrals and numerical analysis.

Mathematical Profile (Excerpt):

• Sergei Lvovich Sobolev studied in the same class as Mikhlin.
• The latter became Mikhlin's master thesis supervisor: the topic of the thesis, defended in 1929, was the convergence of double power series.
• In 1944 Mikhlin returned to Leningrad State University as full professor.
• From 1986 until his death Mikhlin continued as a senior researcher at that laboratory.
• When the Department of Mathematics and Mechanics moved to the Leningrad suburb of Peterhof in 1978, the seminar became more specialized, turning into the seminar of Mikhlin's laboratory on numerical methods.
• In 1961 Mikhlin received the State Order of the Badge of Honour.
• In them is our strength", Mikhlin once said, as reported by Vladimir Maz'ya.
• During the period from 1963 to 1981, Fichera met Mikhlin at several conferences in the Soviet Union, and realised that he was in a state of isolation, later describing several episodes revealing this.
• Perhaps, the most illuminating example is the election of Mikhlin into the Accademia dei Lincei.
• As already mentioned, in June 1981, Solomon G Mikhlin was elected a Foreign Member of the class of Mathematical Sciences of the Academy.
• Thus, Mikhlin was elected as a Foreign Member of the Academy.
• In mathematical elasticity theory, Mikhlin was concerned with three themes: the plane problem (mainly from 1932 to 1935), the theory of shells (from 1954) and the Cosserat spectrum (from 1967 to 1973).
• Mikhlin studied its convergence and gave applications to special applied problems.
• Concerning the theory of shells, there are several Mikhlin's articles dealing with it.
• As a result of his study of this problem, Mikhlin also gave a new invariant form of the basic equations of the theory.
• Mikhlin studied also the spectrum of the operator pencil of the classical Navier-Cauchy operator i.e. the Cosserat spectrum.
• The full description of this spectrum and the proof of the completeness of the system of eigenfunctions are also due to Mikhlin, and partly to Vladimir G Maz'ya in their only joint work.
• In 1961 Mikhlin developed a theory of multidimensional singular integral equations on Lipschitz spaces which are widely used in the theory of one-dimensional singular integral equations.
• However, a direct extension of the related theory to the multidimensional case meets some technical difficulties, and Mikhlin suggested another approach to this problem.
• Mikhlin's multiplier theorem is widely used in different branches of mathematical analysis, particularly in the theory of differential equations.
• Four Mikhlin papers, published in the period 1940-1942, deal with applications of the method of potentials to the mixed problem for the wave equation.
• In 1951 Mikhlin proved the convergence of the Schwarz alternating method for second order elliptic equations.
• The second branch deals with the notion of stability of numerical processes introduced by Mikhlin himself.
• Mikhlin also studied the finite element approximation in weighted Sobolev spaces related to the numerical solution of degenerate elliptic equations.
• During his last years, Mikhlin contributed to the theory of errors in numerical processes, proposing the following classification of errors.
• An active teacher, Mikhlin was the "Kandidat nauk" advisor of a number of mathematicians.
• Mikhlin was also a mentor and friend of Vladimir Maz'ya.

Born 23 April 1908, Kholmech, Belarus. Died 29 August 1990, St Petersburg, Russia.

View full biography at MacTutor

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@Vladimir-G-Maz'ya

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References

Adapted from other CC BY-SA 4.0 Sources:

1. O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive