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Analytical spaces --- Inequalities (Mathematics) --- Sobolev spaces --- 517.518.2 --- Spaces, Sobolev --- Function spaces --- Processes, Infinite --- Classes of functions (sets of functions) --- 517.518.2 Classes of functions (sets of functions) --- Sobolev spaces. --- Sobolev, Espaces de --- Inégalités (mathématiques) --- Sobolev, Espaces de.

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Sobolev Spaces presents an introduction to the theory of Sobolev Spaces and other related spaces of function, also to the imbedding characteristics of these spaces. This theory is widely used in pure and Applied Mathematics and in the Physical Sciences.This second edition of Adam's 'classic' reference text contains many additions and much modernizing and refining of material. The basic premise of the book remains unchanged: Sobolev Spaces is intended to provide a solid foundation in these spaces for graduate students and researchers alike.* Self-contained and acc

Sobolev spaces. --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Calculus --- Spaces, Sobolev --- Function spaces --- Analyse fonctionnelle --- Functional analysis --- Sobolev, Espaces de. --- Sobolev, Espaces de --- ELSEVIER-B EPUB-LIV-FT --- Functional analysis. --- Espaces de sobolev

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The field of variable exponent function spaces has witnessed an explosive growth in recent years. The standard reference article for basic properties is already 20 years old. Thus this self-contained monograph collecting all the basic properties of variable exponent Lebesgue and Sobolev spaces is timely and provides a much-needed accessible reference work utilizing consistent notation and terminology. Many results are also provided with new and improved proofs. The book also presents a number of applications to PDE and fluid dynamics.

Function spaces --- Sobolev spaces --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Applied Mathematics --- Sobolev spaces. --- Lebesgue integral. --- Integration, Lebesgue --- L-integral --- Lebesgue integration --- Lebesgue-Stieltjes integral --- Lebesgue's integral --- Stieltjes integral, Lebesgue --- -Spaces, Sobolev --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Functional analysis. --- Partial differential equations. --- Analysis. --- Functional Analysis. --- Partial Differential Equations. --- Partial differential equations --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- 517.1 Mathematical analysis --- Mathematical analysis --- Math --- Science --- -Integrals, Generalized --- Measure theory --- Spaces, Sobolev --- Global analysis (Mathematics). --- Differential equations, partial. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic

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Sobolev spaces play an outstanding role in modern analysis, in particular, in the theory of partial differential equations and its applications in mathematical physics. They form an indispensable tool in approximation theory, spectral theory, differential geometry etc. The theory of these spaces is of interest in itself being a beautiful domain of mathematics. The present volume includes basics on Sobolev spaces, approximation and extension theorems, embedding and compactness theorems, their relations with isoperimetric and isocapacitary inequalities, capacities with applications to spectral theory of elliptic differential operators as well as pointwise inequalities for derivatives. The selection of topics is mainly influenced by the author’s involvement in their study, a considerable part of the text is a report on his work in the field. Part of this volume first appeared in German as three booklets of Teubner-Texte zur Mathematik (1979,1980). In the Springer volume “Sobolev Spaces”, published in English in 1985, the material was expanded and revised. The present 2nd edition is enhanced by many recent results and it includes new applications to linear and nonlinear partial differential equations. New historical comments, five new chapters and a significantly augmented list of references aim to create a broader and modern view of the area.

Electronic books. -- local. --- Functional analysis. --- Sobolev spaces. --- Sobolev spaces --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Applied Mathematics --- Calculus --- Functional calculus --- Spaces, Sobolev --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Analysis. --- Calculus of variations --- Functional equations --- Integral equations --- Function spaces --- Global analysis (Mathematics). --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- 517.1 Mathematical analysis --- Mathematical analysis

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The book systematically develops the nonlinear potential theory connected with the weighted Sobolev spaces, where the weight usually belongs to Muckenhoupt's class of Ap weights. These spaces occur as solutions spaces for degenerate elliptic partial differential equations. The Sobolev space theory covers results concerning approximation, extension, and interpolation, Sobolev and Poincaré inequalities, Maz'ya type embedding theorems, and isoperimetric inequalities. In the chapter devoted to potential theory, several weighted capacities are investigated. Moreover, "Kellogg lemmas" are established for various concepts of thinness. Applications of potential theory to weighted Sobolev spaces include quasi continuity of Sobolev functions, Poincaré inequalities, and spectral synthesis theorems.

Potential theory (Mathematics) --- Nonlinear theories --- Sobolev spaces --- Espaces de Sobolev --- Niet-lineaire theorieën --- Potentiaaltheorie --- Potentiel [Théorie du ] --- Ruimten van Sobolev --- Sobolev [Espaces de ] --- Sobolev [Ruimten van ] --- Spaces [Sobolev ] --- Theorieën [Niet-lineaire ] --- Théories non-linéaires --- Potential theory (Mathematics). --- Partial differential equations. --- Potential Theory. --- Partial Differential Equations. --- Partial differential equations --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics