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About An Introduction to Sobolev Spaces
Sobolev spaces were firstly defined by the Russian mathematician S L Sobolev 1908 1989 in the 1930s Several properties of these spaces have been studied by mathematicians till today Especially 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 This book provides a brief introduction to Sobolev spaces at a simple level with illustrated examples Some of their applications might be relevant both to undergraduate and graduate students mathematicians and engineers who have an interest in getting a quick but carefully presented mathematically sound basic knowledge in this domain In this regard the book fills an important gap in that field There are seven chapters in the book The first chapter is devoted to basic concepts consisting of metric spaces normed spaces inner product spaces Hilbert spaces and some important results on fixed point theorems The second chapter is based on Lp spaces Several important inequalities embedding property of Lp and some other spaces are presented in this part In chapter three we introduce the notion of the weak derivative There are many numerical example in order the reader to distinguish the weak derivative from the classical one Sobolev spaces are presented and widely analyzed in chapter four Chapter five is devoted to Sobolev embedding theorems The variable exponent Lebesgue and Sobolev spaces are investigated in chapter six Finally in chapter seven we present the importance of Sobolev spaces in light of their application to some differential equations
Detailed Information
| Author: | Baver Okutmustur |
|---|---|
| Publication Year: | 2021 |
| ISBN: | 9781681089133 |
| Pages: | 203 |
| Language: | English |
| File Size: | 8.2 |
| Format: | |
| Price: | FREE |
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