Sobolev Spaces

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Author: Robert A. Adams
Publisher: Elsevier
ISBN: 9780080541297
Size: 66.88 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: 49.49 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

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Author: Giovanni Leoni
Publisher: American Mathematical Soc.
ISBN: 0821847686
Size: 17.73 MB
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A First Course In Sobolev Spaces by Giovanni Leoni


Original Title: A First Course In Sobolev Spaces

Sobolev spaces are a fundamental tool in the modern study of partial differential equations. In this book, Leoni takes a novel approach to the theory by looking at Sobolev spaces as the natural development of monotone, absolutely continuous, and BV functions of one variable. In this way, the majority of the text can be read without the prerequisite of a course in functional analysis. The first part of this text is devoted to studying functions of one variable. Several of the topics treated occur in courses on real analysis or measure theory. Here, the perspective emphasizes their applications to Sobolev functions, giving a very different flavor to the treatment. This elementary start to the book makes it suitable for advanced undergraduates or beginning graduate students. Moreover, the one-variable part of the book helps to develop a solid background that facilitates the reading and understanding of Sobolev functions of several variables. The second part of the book is more classical, although it also contains some recent results. Besides the standard results on Sobolev functions, this part of the book includes chapters on BV functions, symmetric rearrangement, and Besov spaces. The book contains over 200 exercises.

Nonlinear Potential Theory And Weighted Sobolev Spaces

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Author: Bengt O. Turesson
Publisher: Springer
ISBN: 3540451684
Size: 55.71 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 I

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Author: Vladimir Maz'ya
Publisher: Springer Science & Business Media
ISBN: 038785648X
Size: 72.25 MB
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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.

Lectures On Elliptic And Parabolic Equations In Sobolev Spaces

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Author: Nikolaĭ Vladimirovich Krylov
Publisher: American Mathematical Soc.
ISBN: 0821846841
Size: 40.24 MB
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Lectures On Elliptic And Parabolic Equations In Sobolev Spaces by Nikolaĭ Vladimirovich Krylov


Original Title: Lectures On Elliptic And Parabolic Equations In Sobolev Spaces

This book concentrates on the basic facts and ideas of the modern theory of linear elliptic and parabolic equations in Sobolev spaces. The main areas covered in this book are the first boundary-value problem for elliptic equations and the Cauchy problem for parabolic equations. In addition, other boundary-value problems such as the Neumann or oblique derivative problems are briefly covered. As is natural for a textbook, the main emphasis is on organizing well-known ideas in a self-contained exposition. Among the topics included that are not usually covered in a textbook are a relatively recent development concerning equations with $\mathsf{VMO}$ coefficients and the study of parabolic equations with coefficients measurable only with respect to the time variable. There are numerous exercises which help the reader better understand the material. After going through the book, the reader will have a good understanding of results available in the modern theory of partial differential equations and the technique used to obtain them. Prerequisites are basics of measure theory, the theory of $L_p$ spaces, and the Fourier transform.

An Introduction To Sobolev Spaces And Interpolation Spaces

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Author: Luc Tartar
Publisher: Springer Science & Business Media
ISBN: 3540714839
Size: 13.94 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: 60.35 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.

Sobolev Spaces Their Generalizations And Elliptic Problems In Smooth And Lipschitz Domains

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Author: Mikhail S. Agranovich
Publisher: Springer
ISBN: 3319146483
Size: 57.83 MB
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Sobolev Spaces Their Generalizations And Elliptic Problems In Smooth And Lipschitz Domains by Mikhail S. Agranovich


Original Title: Sobolev Spaces Their Generalizations And Elliptic Problems In Smooth And Lipschitz Domains

This book, which is based on several courses of lectures given by the author at the Independent University of Moscow, is devoted to Sobolev-type spaces and boundary value problems for linear elliptic partial differential equations. Its main focus is on problems in non-smooth (Lipschitz) domains for strongly elliptic systems. The author, who is a prominent expert in the theory of linear partial differential equations, spectral theory and pseudodifferential operators, has included his own very recent findings in the present book. The book is well suited as a modern graduate textbook, utilizing a thorough and clear format that strikes a good balance between the choice of material and the style of exposition. It can be used both as an introduction to recent advances in elliptic equations and boundary value problems and as a valuable survey and reference work. It also includes a good deal of new and extremely useful material not available in standard textbooks to date. Graduate and post-graduate students, as well as specialists working in the fields of partial differential equations, functional analysis, operator theory and mathematical physics will find this book particularly valuable.

Sobolev Spaces In Mathematics Ii

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Author: Vladimir Maz'ya
Publisher: Springer Science & Business Media
ISBN: 0387856501
Size: 79.39 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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