Bentham Science Publishers, Sharjah, 2021
Sobolev spaces were firstly defined by the Russian mathematician, Sergei
L. Sobolev (1908-1989) in the 1930s. Several properties of these spaces
have been studied by mathematicians until today. Functions that account
for existence and uniqueness, asymptotic behavior, blow up, stability
and instability of the solution of many differential equations that
occur in applied and in engineering sciences are carried out with the
help of Sobolev spaces and embedding theorems in these spaces.
An Introduction to Sobolev Spaces provides a brief introduction to
Sobolev spaces at a simple level with illustrated examples. Readers will
learn about the properties of these types of vector spaces and gain an
understanding of advanced differential calculus and partial difference
equations that are related to this topic. The contents of the book are
suitable for undergraduate and graduate students, mathematicians, and
engineers who have an interest in getting a quick, but carefully
presented, mathematically sound, basic knowledge about Sobolev Spaces.