Weakly Differentiable Functions: Sobolev Spaces and Functions of Bounded Variation (Graduate Texts in Mathematics) [Hardcover]

William P. Ziemer (Author)

Book Description

Publication Date: September 18, 1989 | ISBN-10: 0387970177 | ISBN-13: 978-0387970172 | Edition: 1

The major thrust of this book is the analysis of pointwise behavior of Sobolev functions of integer order and BV functions (functions whose partial derivatives are measures with finite total variation). The development of Sobolev functions includes an analysis of their continuity properties in terms of Lebesgue points, approximate continuity, and fine continuity as well as a discussion of their higher order regularity properties in terms of Lp-derivatives. This provides the foundation for further results such as a strong approximation theorem and the comparison of Lp and distributional derivatives. Also included is a treatment of Sobolev-Poincaré type inequalities which unifies virtually all inequalities of this type. Although the techniques required for the discussion of BV functions are completely different from those required for Sobolev functions, there are similarities between their developments such as a unifying treatment of Poincaré-type inequalities for BV functions. This book is intended for graduate students and researchers whose interests may include aspects of approximation theory, the calculus of variations, partial differential equations, potential theory and related areas. The only prerequisite is a standard graduate course in real analysis since almost all of the material is accessible through real variable techniques.

Product Details

• Hardcover: 348 pages
• Publisher: Springer; 1 edition (September 18, 1989)
• Language: English
• ISBN-10: 0387970177
• ISBN-13: 978-0387970172
• Product Dimensions: 9.3 x 6 x 0.9 inches
• Shipping Weight: 1.4 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #802,969 in Books (See Top 100 in Books)

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9 of 9 people found the following review helpful:

5.0 out of 5 stars excellent resource, January 6, 2000

By A Customer

This review is from: Weakly Differentiable Functions: Sobolev Spaces and Functions of Bounded Variation (Graduate Texts in Mathematics) (Hardcover)

The function spaces discussed in this book are the natural ones in which to look for solutions of Partial Differential Equations and of problems in the Calculus of Variations (and so I don't think the material is esoteric!). This book is simply necessary for analysts and for anyone interested in rigor in the context of PDE. It is not as readable as the book by Evans and Gariepy, which is a pleasure to read cover to cover, but it contains more information and discusses some more technical spaces.