Young measures and compactness in measure spaces / Liviu C. Florescu, Christiane Godet-Thobie.

Format:

Book

Author/Creator:

Florescu, Liviu C.

Contributor:

Godet-Thobie, Christiane.

Language:

English

Subjects (All):

Spaces of measures.

Measure theory.

Mathematical optimization.

Physical Description:

1 online resource (352 p.)

Edition:

1st ed.

Place of Publication:

Berlin ; Boston : De Gruyter, c2012.

Language Note:

English

Summary:

In recent years, technological progress created a great need for complex mathematical models. Many practical problems can be formulated using optimization theory and they hope to obtain an optimal solution. In most cases, such optimal solution can not be found. So, non-convex optimization problems (arising, e.g., in variational calculus, optimal control, nonlinear evolutions equations) may not possess a classical minimizer because the minimizing sequences have typically rapid oscillations. This behavior requires a relaxation of notion of solution for such problems; often we can obtain such a relaxation by means of Young measures. This monograph is a self-contained book which gathers all theoretical aspects related to the defining of Young measures (measurability, disintegration, stable convergence, compactness), a book which is also a useful tool for those interested in theoretical foundations of the measure theory. It provides a complete set of classical and recent compactness results in measure and function spaces. The book is organized in three chapters: The first chapter covers background material on measure theory in abstract frame. In the second chapter the measure theory on topological spaces is presented. Compactness results from the first two chapters are used to study Young measures in the third chapter. All results are accompanied by full demonstrations and for many of these results different proofs are given. All statements are fully justified and proved.

Contents:

Front matter

Preface

Contents

Chapter 1. Weak Compactness in Measure Spaces

Chapter 2. Bounded Measures on Topological Spaces

Chapter 3. Young Measures

Bibliography

Index

About the Authors

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9781283857918

128385791X

9783110280517

3110280515

9783110280524

3110280523

OCLC:

796384258