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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis
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Nonlinear Analysis on Manifolds - Sobolev Spaces and Inequalities (Paperback)
Loot Price: R924
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Nonlinear Analysis on Manifolds - Sobolev Spaces and Inequalities (Paperback)
Series: Courant Lecture Notes
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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.
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