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Author: Emmanuel Hebey
Publisher: Springer
ISBN: 3540699937
Category : Mathematics
Languages : en
Pages : 126
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Book Description
Several books deal with Sobolev spaces on open subsets of R (n), but none yet with Sobolev spaces on Riemannian manifolds, despite the fact that the theory of Sobolev spaces on Riemannian manifolds already goes back about 20 years. The book of Emmanuel Hebey will fill this gap, and become a necessary reading for all using Sobolev spaces on Riemannian manifolds. Hebey's presentation is very detailed, and includes the most recent developments due mainly to the author himself and to Hebey-Vaugon. He makes numerous things more precise, and discusses the hypotheses to test whether they can be weakened, and also presents new results.
Author: Emmanuel Hebey
Publisher: Springer
ISBN: 3540699937
Category : Mathematics
Languages : en
Pages : 126
Get Book
Book Description
Several books deal with Sobolev spaces on open subsets of R (n), but none yet with Sobolev spaces on Riemannian manifolds, despite the fact that the theory of Sobolev spaces on Riemannian manifolds already goes back about 20 years. The book of Emmanuel Hebey will fill this gap, and become a necessary reading for all using Sobolev spaces on Riemannian manifolds. Hebey's presentation is very detailed, and includes the most recent developments due mainly to the author himself and to Hebey-Vaugon. He makes numerous things more precise, and discusses the hypotheses to test whether they can be weakened, and also presents new results.
Author: Emmanuel Hebey
Publisher: Springer Science & Business Media
ISBN: 9783540617228
Category : Mathematics
Languages : en
Pages : 134
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Book Description
Several books deal with Sobolev spaces on open subsets of R (n), but none yet with Sobolev spaces on Riemannian manifolds, despite the fact that the theory of Sobolev spaces on Riemannian manifolds already goes back about 20 years. The book of Emmanuel Hebey will fill this gap, and become a necessary reading for all using Sobolev spaces on Riemannian manifolds. Hebey's presentation is very detailed, and includes the most recent developments due mainly to the author himself and to Hebey-Vaugon. He makes numerous things more precise, and discusses the hypotheses to test whether they can be weakened, and also presents new results.
Author: Emmanuel Hebey
Publisher: American Mathematical Soc.
ISBN: 0821827006
Category : Mathematics
Languages : en
Pages : 306
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Book Description
This volume offers an expanded version of lectures given at the Courant Institute on the theory of Sobolev spaces on Riemannian manifolds. ``Several surprising phenomena appear when studying Sobolev spaces on manifolds,'' according to the author. ``Questions that are elementary for Euclidean space become challenging and give rise to sophisticated mathematics, where the geometry of the manifold plays a central role.'' The volume is organized into nine chapters. Chapter 1 offers a brief introduction to differential and Riemannian geometry. Chapter 2 deals with the general theory of Sobolev spaces for compact manifolds. Chapter 3 presents the general theory of Sobolev spaces for complete, noncompact manifolds. Best constants problems for compact manifolds are discussed in Chapters 4 and 5. Chapter 6 presents special types of Sobolev inequalities under constraints. Best constants problems for complete noncompact manifolds are discussed in Chapter 7. Chapter 8 deals with Euclidean-type Sobolev inequalities. And Chapter 9 discusses the influence of symmetries on Sobolev embeddings. An appendix offers brief notes on the case of manifolds with boundaries. This topic is a field undergoing great development at this time. However, several important questions remain open. So a substantial part of the book is devoted to the concept of best constants, which appeared to be crucial for solving limiting cases of some classes of PDEs. The volume is highly self-contained. No familiarity is assumed with differentiable manifolds and Riemannian geometry, making the book accessible to a broad audience of readers, including graduate students and researchers.
Author: Hans Triebel
Publisher: Springer Science & Business Media
ISBN: 3034604181
Category : Juvenile Nonfiction
Languages : en
Pages : 375
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Book Description
Theory of Function Spaces II deals with the theory of function spaces of type Bspq and Fspq as it stands at the present. These two scales of spaces cover many well-known function spaces such as Hölder-Zygmund spaces, (fractional) Sobolev spaces, Besov spaces, inhomogeneous Hardy spaces, spaces of BMO-type and local approximation spaces which are closely connected with Morrey-Campanato spaces. Theory of Function Spaces II is self-contained, although it may be considered an update of the author’s earlier book of the same title. The book’s 7 chapters start with a historical survey of the subject, and then analyze the theory of function spaces in Rn and in domains, applications to (exotic) pseudo-differential operators, and function spaces on Riemannian manifolds. ------ Reviews The first chapter deserves special attention. This chapter is both an outstanding historical survey of function spaces treated in the book and a remarkable survey of rather different techniques developed in the last 50 years. It is shown that all these apparently different methods are only different ways of characterizing the same classes of functions. The book can be best recommended to researchers and advanced students working on functional analysis. - Zentralblatt MATH
Author: Jürgen Eichhorn
Publisher: Nova Publishers
ISBN: 9781600215636
Category : Mathematics
Languages : en
Pages : 664
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Book Description
Global analysis is the analysis on manifolds. Since the middle of the sixties there exists a highly elaborated setting if the underlying manifold is compact, evidence of which can be found in index theory, spectral geometry, the theory of harmonic maps, many applications to mathematical physics on closed manifolds like gauge theory, Seiberg-Witten theory, etc. If the underlying manifold is open, i.e. non-compact and without boundary, then most of the foundations and of the great achievements fail. Elliptic operators are no longer Fredholm, the analytical and topological indexes are not defined, the spectrum of self-adjoint elliptic operators is no longer discrete, functional spaces strongly depend on the operators involved and the data from geometry, many embedding and module structure theorems do not hold, manifolds of maps are not defined, etc. It is the goal of this new book to provide serious foundations for global analysis on open manifolds, to discuss the difficulties and special features which come from the openness and to establish many results and applications on this basis.
Author: Vladimir Maz'ya
Publisher: Springer Science & Business Media
ISBN: 0387856501
Category : Mathematics
Languages : en
Pages : 404
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Book Description
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.
Author: Vladimir Maz'ya
Publisher: Springer
ISBN: 3662099225
Category : Mathematics
Languages : en
Pages : 506
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Book Description
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
Author: Steven Rosenberg
Publisher: Cambridge University Press
ISBN: 9780521468312
Category : Mathematics
Languages : en
Pages : 190
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Book Description
This text on analysis of Riemannian manifolds is aimed at students who have had a first course in differentiable manifolds.
Author: Vladimir Maz'ya
Publisher: Springer Science & Business Media
ISBN: 038785648X
Category : Mathematics
Languages : en
Pages : 395
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Book Description
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.
Author: Yvonne Choquet-Bruhat
Publisher: Gulf Professional Publishing
ISBN: 9780444860170
Category : Mathematics
Languages : en
Pages : 666
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Book Description
This reference book, which has found wide use as a text, provides an answer to the needs of graduate physical mathematics students and their teachers. The present edition is a thorough revision of the first, including a new chapter entitled ``Connections on Principle Fibre Bundles'' which includes sections on holonomy, characteristic classes, invariant curvature integrals and problems on the geometry of gauge fields, monopoles, instantons, spin structure and spin connections. Many paragraphs have been rewritten, and examples and exercises added to ease the study of several chapters. The index includes over 130 entries.
