Sergei Lvovich Sobolev
Encyclopedia
Sergei Lvovich Sobolev was a Soviet mathematician
working in mathematical analysis
and partial differential equation
s. He was born in St. Petersburg
, and died in Moscow
.
s can be defined by some growth conditions on the Fourier transform
s; they and their embedding theorems are an important subject in functional analysis
. Generalized function
s (later known as distribution
s) were first introduced by Sobolev in 1935 for weak solution
s, and further developed by Laurent Schwartz
. Sobolev abstracted the classical notion of differentiation
so expanding the ranges of applications of the technique of Newton and Leibniz. The theory of distribution
is considered now as the calculus of the modern epoch.
in 1929, where he was a student of Nikolai Maksimovich Günter. After graduation he worked with Vladimir Smirnov whom he considered as his second teacher. He worked in Leningrad from 1932, and at the Steklov Institute of Mathematics
in Moscow from 1934. He headed the institute in evacuation to Kazan
during the World War II
. He was a Moscow State University
professor from 1935 to 1957 and also a deputy director of the Institute for Atomic Energy
1943-57 where he participated in the A-bomb project of the USSR.
In 1956 Sobolev joined a number of prominent scientists in proposing a large-scale scientific and educational initiative for the Eastern parts of the Soviet Union
, which resulted in the creation of the Siberian Division of the Academy of Sciences
. He was the founder and first director of the Institute of Mathematics at Akademgorodok
near Novosibirsk
, which was later to bear his name, and played an important role in the establishment and development of Novosibirsk State University
.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
working in mathematical analysis
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
and partial differential equation
Partial differential equation
In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...
s. He was born in St. Petersburg
Saint Petersburg
Saint Petersburg is a city and a federal subject of Russia located on the Neva River at the head of the Gulf of Finland on the Baltic Sea...
, and died in Moscow
Moscow
Moscow is the capital, the most populous city, and the most populous federal subject of Russia. The city is a major political, economic, cultural, scientific, religious, financial, educational, and transportation centre of Russia and the continent...
.
Work
Sobolev introduced the notions that are now fundamental for several different areas of mathematics. Sobolev spaceSobolev space
In mathematics, a Sobolev space is a vector space of functions equipped with a norm that is a combination of Lp-norms of the function itself as well as its derivatives up to a given order. The derivatives are understood in a suitable weak sense to make the space complete, thus a Banach space...
s can be defined by some growth conditions on the Fourier transform
Fourier transform
In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...
s; they and their embedding theorems are an important subject in functional analysis
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
. Generalized function
Generalized function
In mathematics, generalized functions are objects generalizing the notion of functions. There is more than one recognized theory. Generalized functions are especially useful in making discontinuous functions more like smooth functions, and describing physical phenomena such as point charges...
s (later known as distribution
Distribution (mathematics)
In mathematical analysis, distributions are objects that generalize functions. Distributions make it possible to differentiate functions whose derivatives do not exist in the classical sense. In particular, any locally integrable function has a distributional derivative...
s) were first introduced by Sobolev in 1935 for weak solution
Weak solution
In mathematics, a weak solution to an ordinary or partial differential equation is a function for which the derivatives may not all exist but which is nonetheless deemed to satisfy the equation in some precisely defined sense. There are many different definitions of weak solution, appropriate for...
s, and further developed by Laurent Schwartz
Laurent Schwartz
Laurent-Moïse Schwartz was a French mathematician. He pioneered the theory of distributions, which gives a well-defined meaning to objects such as the Dirac delta function. He was awarded the Fields medal in 1950 for his work...
. Sobolev abstracted the classical notion of differentiation
Derivative
In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a...
so expanding the ranges of applications of the technique of Newton and Leibniz. The theory of distribution
Distribution (mathematics)
In mathematical analysis, distributions are objects that generalize functions. Distributions make it possible to differentiate functions whose derivatives do not exist in the classical sense. In particular, any locally integrable function has a distributional derivative...
is considered now as the calculus of the modern epoch.
Life
Sobolev graduated from Leningrad UniversitySaint Petersburg State University
Saint Petersburg State University is a Russian federal state-owned higher education institution based in Saint Petersburg and one of the oldest and largest universities in Russia....
in 1929, where he was a student of Nikolai Maksimovich Günter. After graduation he worked with Vladimir Smirnov whom he considered as his second teacher. He worked in Leningrad from 1932, and at the Steklov Institute of Mathematics
Steklov Institute of Mathematics
Steklov Institute of Mathematics or Steklov Mathematical Institute is a research institute based in Moscow, specialized in mathematics, and a part of the Russian Academy of Sciences. It was established April 24, 1934 by the decision of the General Assembly of the Academy of Sciences of the USSR in...
in Moscow from 1934. He headed the institute in evacuation to Kazan
Kazan
Kazan is the capital and largest city of the Republic of Tatarstan, Russia. With a population of 1,143,546 , it is the eighth most populous city in Russia. Kazan lies at the confluence of the Volga and Kazanka Rivers in European Russia. In April 2009, the Russian Patent Office granted Kazan the...
during the World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
. He was a Moscow State University
Moscow State University
Lomonosov Moscow State University , previously known as Lomonosov University or MSU , is the largest university in Russia. Founded in 1755, it also claims to be one of the oldest university in Russia and to have the tallest educational building in the world. Its current rector is Viktor Sadovnichiy...
professor from 1935 to 1957 and also a deputy director of the Institute for Atomic Energy
Kurchatov Institute
The Kurchatov Institute is Russia's leading research and development institution in the field of nuclear energy. In the Soviet Union it was known as I. V. Kurchatov Institute of Atomic Energy , abbreviated KIAE . It is named after Igor Kurchatov....
1943-57 where he participated in the A-bomb project of the USSR.
In 1956 Sobolev joined a number of prominent scientists in proposing a large-scale scientific and educational initiative for the Eastern parts of the Soviet Union
Soviet Union
The Soviet Union , officially the Union of Soviet Socialist Republics , was a constitutionally socialist state that existed in Eurasia between 1922 and 1991....
, which resulted in the creation of the Siberian Division of the Academy of Sciences
Russian Academy of Sciences
The Russian Academy of Sciences consists of the national academy of Russia and a network of scientific research institutes from across the Russian Federation as well as auxiliary scientific and social units like libraries, publishers and hospitals....
. He was the founder and first director of the Institute of Mathematics at Akademgorodok
Akademgorodok
Akademgorodok , is a part of the Russian city Novosibirsk, located 20 km south of the city center. It is the educational and scientific centre of Siberia...
near Novosibirsk
Novosibirsk
Novosibirsk is the third-largest city in Russia, after Moscow and Saint Petersburg, and the largest city of Siberia, with a population of 1,473,737 . It is the administrative center of Novosibirsk Oblast as well as of the Siberian Federal District...
, which was later to bear his name, and played an important role in the establishment and development of Novosibirsk State University
Novosibirsk State University
Novosibirsk State University was founded in May 1959 in the USSR by Soviet academicians Mikhail Alekseevich Lavrentiev, Sergei Lvovich Sobolev and Sergey Alekseyevich Khristianovich in a program of establishing a Siberian branch of the USSR Academy of Sciences...
.
See also
- Sobolev conjugate
- Sobolev embedding theorem
- Sobolev generalized derivativeWeak derivativeIn mathematics, a weak derivative is a generalization of the concept of the derivative of a function for functions not assumed differentiable, but only integrable, i.e. to lie in the Lebesgue space L^1. See distributions for an even more general definition.- Definition :Let u be a function in the...
- Sobolev inequalitySobolev inequalityIn mathematics, there is in mathematical analysis a class of Sobolev inequalities, relating norms including those of Sobolev spaces. These are used to prove the Sobolev embedding theorem, giving inclusions between certain Sobolev spaces, and the Rellich–Kondrachov theorem showing that under...
- Sobolev spaceSobolev spaceIn mathematics, a Sobolev space is a vector space of functions equipped with a norm that is a combination of Lp-norms of the function itself as well as its derivatives up to a given order. The derivatives are understood in a suitable weak sense to make the space complete, thus a Banach space...