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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.

Sobolev spaces. --- Interpolation spaces. --- Differential equations, Partial. --- Partial differential equations --- Spaces, Interpolation --- Function spaces --- Spaces, Sobolev

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Differential equations --- Mathematical physics --- Computer. Automation --- differentiaalvergelijkingen --- informatica --- wiskunde --- fysica --- Mathematical physics. --- Differential equations, Partial. --- Mathematics --- Data processing. --- Partial differential equations --- Physical mathematics --- Physics

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Differential equations, Parabolic. --- Differential equations, Elliptic. --- Elliptic differential equations --- Elliptic partial differential equations --- Linear elliptic differential equations --- Differential equations, Linear --- Differential equations, Partial --- Parabolic differential equations --- Parabolic partial differential equations

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Mathematical analysis --- Numerical analysis --- Mathematics --- Mathematical physics --- Applied physical engineering --- Engineering sciences. Technology --- Computer. Automation --- ICT (informatie- en communicatietechnieken) --- analyse (wiskunde) --- toegepaste wiskunde --- theoretische fysica --- economie --- informatica --- wiskunde --- ingenieurswetenschappen --- fysica --- numerieke analyse --- Differential equations, Partial --- Numerical solutions. --- Equacions en derivades parcials --- Solucions numèriques --- Anàlisi numèrica --- EDPs --- Equació diferencial en derivades parcials --- Equacions diferencials en derivades parcials --- Equacions diferencials parcials --- Equacions diferencials --- Dispersió (Matemàtica) --- Equació d'ona --- Equació de Dirac --- Equació de Fokker-Planck --- Equació de Schrödinger --- Equacions de Navier-Stokes --- Equacions de Hamilton-Jacobi --- Equacions de Maxwell --- Equacions de Monge-Ampère --- Equacions de Von Kármán --- Equacions diferencials el·líptiques --- Equacions diferencials hiperbòliques --- Equacions diferencials parabòliques --- Equacions diferencials parcials estocàstiques --- Funcions harmòniques --- Laplacià --- Problema de Cauchy --- Problema de Neumann --- Teoria espectral (Matemàtica)