Sobolev Spaces

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Author: Robert A. Adams
Publisher: Elsevier
ISBN: 9780080541297
Size: 32.78 MB
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Sobolev Spaces by Robert A. Adams


Original Title: Sobolev Spaces

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 accessible for readers in other disciplines Written at elementary level making it accessible to graduate students

Sobolev Spaces

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Author: Vladimir Maz'ya
Publisher: Springer
ISBN: 3662099225
Size: 72.73 MB
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Sobolev Spaces by Vladimir Maz'ya


Original Title: Sobolev Spaces

The Sobolev spaces, i. e. the classes of functions with derivatives in L , occupy p an outstanding place in analysis. During the last two decades a substantial contribution to the study of these spaces has been made; so now solutions to many important problems connected with them are known. In the present monograph we consider various aspects of Sobolev space theory. Attention is paid mainly to the so called imbedding theorems. Such theorems, originally established by S. L. Sobolev in the 1930s, proved to be a useful tool in functional analysis and in the theory of linear and nonlinear par tial differential equations. We list some questions considered in this book. 1. What are the requirements on the measure f1, for the inequality q

A First Course In Sobolev Spaces Second Edition

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Author: Giovanni Leoni
Publisher: American Mathematical Soc.
ISBN: 1470429217
Size: 59.76 MB
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A First Course In Sobolev Spaces Second Edition by Giovanni Leoni


Original Title: A First Course In Sobolev Spaces Second Edition

This book is about differentiation of functions. It is divided into two parts, which can be used as different textbooks, one for an advanced undergraduate course in functions of one variable and one for a graduate course on Sobolev functions. The first part develops the theory of monotone, absolutely continuous, and bounded variation functions of one variable and their relationship with Lebesgue–Stieltjes measures and Sobolev functions. It also studies decreasing rearrangement and curves. The second edition includes a chapter on functions mapping time into Banach spaces. The second part of the book studies functions of several variables. It begins with an overview of classical results such as Rademacher's and Stepanoff's differentiability theorems, Whitney's extension theorem, Brouwer's fixed point theorem, and the divergence theorem for Lipschitz domains. It then moves to distributions, Fourier transforms and tempered distributions. The remaining chapters are a treatise on Sobolev functions. The second edition focuses more on higher order derivatives and it includes the interpolation theorems of Gagliardo and Nirenberg. It studies embedding theorems, extension domains, chain rule, superposition, Poincaré's inequalities and traces. A major change compared to the first edition is the chapter on Besov spaces, which are now treated using interpolation theory.

Sobolev Spaces In Mathematics I

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Author: Vladimir Maz'ya
Publisher: Springer Science & Business Media
ISBN: 038785648X
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Sobolev Spaces In Mathematics I by Vladimir Maz'ya


Original Title: Sobolev Spaces In Mathematics I

This volume mark’s the centenary of the birth of the outstanding mathematician of the 20th century, Sergey Sobolev. It includes new results on the latest topics of the theory of Sobolev spaces, partial differential equations, analysis and mathematical physics.

An Introduction To Sobolev Spaces And Interpolation Spaces

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Author: Luc Tartar
Publisher: Springer Science & Business Media
ISBN: 3540714839
Size: 50.76 MB
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An Introduction To Sobolev Spaces And Interpolation Spaces by Luc Tartar


Original Title: An Introduction To Sobolev Spaces And Interpolation Spaces

After publishing an introduction to the Navier–Stokes equation and oceanography (Vol. 1 of this series), Luc Tartar follows with another set of lecture notes based on a graduate course in two parts, as indicated by the title. A draft has been available on the internet for a few years. The author has now revised and polished it into a text accessible to a larger audience.

Functional Analysis Sobolev Spaces And Partial Differential Equations

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Author: Haim Brezis
Publisher: Springer Science & Business Media
ISBN: 0387709134
Size: 70.37 MB
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Functional Analysis Sobolev Spaces And Partial Differential Equations by Haim Brezis


Original Title: Functional Analysis Sobolev Spaces And Partial Differential Equations

This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.

Nonlinear Potential Theory And Weighted Sobolev Spaces

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Author: Bengt O. Turesson
Publisher: Springer
ISBN: 3540451684
Size: 31.48 MB
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Nonlinear Potential Theory And Weighted Sobolev Spaces by Bengt O. Turesson


Original Title: Nonlinear Potential Theory And Weighted Sobolev Spaces

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.

Sobolev Spaces In Mathematics Ii

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Author: Vladimir Maz'ya
Publisher: Springer Science & Business Media
ISBN: 0387856501
Size: 38.46 MB
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Sobolev Spaces In Mathematics Ii by Vladimir Maz'ya


Original Title: Sobolev Spaces In Mathematics Ii

Sobolev spaces become the established and universal language of partial differential equations and mathematical analysis. Among a huge variety of problems where Sobolev spaces are used, the following important topics are the focus of this volume: boundary value problems in domains with singularities, higher order partial differential equations, local polynomial approximations, inequalities in Sobolev-Lorentz spaces, function spaces in cellular domains, the spectrum of a Schrodinger operator with negative potential and other spectral problems, criteria for the complete integration of systems of differential equations with applications to differential geometry, some aspects of differential forms on Riemannian manifolds related to Sobolev inequalities, Brownian motion on a Cartan-Hadamard manifold, etc. Two short biographical articles on the works of Sobolev in the 1930s and the foundation of Akademgorodok in Siberia, supplied with unique archive photos of S. Sobolev are included.

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