A first course in Sobolev spaces / Giovanni Leoni.

Format:

Book

Author/Creator:

Leoni, Giovanni, 1967- author.

Series:

Graduate studies in mathematics ; Volume 105.

Graduate Studies in Mathematics ; Volume 105

Language:

English

Subjects (All):

Sobolev spaces.

Physical Description:

1 online resource (607 p.)

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2009.

Language Note:

English

Summary:

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.

Contents:

Part I. Functions of one variable

Monotone functions

Functions of bounded pointwise variation

Absolutely continuous functions

Curves

Lebesgue�Stieltjes measures

Decreasing rearrangement

Functions of bounded variation and Sobolev functions

Part II. Functions of several variables

Absolutely continuous functions and change of variables

Distributions

Sobolev spaces

Sobolev spaces: Embeddings

Sobolev spaces: Further properties

Functions of bounded variation

Besov spaces

Sobolev spaces: Traces

Sobolev spaces: Symmetrization

Functional analysis

Measures

The Lebesgue and Hausdorff measures.

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-4704-1169-5