Parametrized measures and variational principles
The purpose of this book is to present a new approach to fundamental questions concerning the calculus of variations (and more generally to the theory of optimization) based on a systematic analysis of Young measures. Weak lower semicontinuity and relaxation are main areas of concentration in this work. The unified treatment of scalar and vector cases developed here is suitable also for more general situations. Applications to problems in continuum mechanics and nonlinear elasticity are analyze…
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- Full title :Parametrized measures and variational principles / Pablo Pedregal.
Summary
The purpose of this book is to present a new approach to fundamental questions concerning the calculus of variations (and more generally to the theory of optimization) based on a systematic analysis of Young measures. Weak lower semicontinuity and relaxation are main areas of concentration in this work. The unified treatment of scalar and vector cases developed here is suitable also for more general situations. Applications to problems in continuum mechanics and nonlinear elasticity are analyzed in some depth. Other problems are included to motivate interest in Young measures and to emphasize the wide range of applicability of these techniques (to, for example, optimal control, optimal design and turbulence). Researchers and graduate students in applied mathematics and mechanics will benefit from this general approach to variational principles.
Read More ↓Edition Statements
- Publication Date:©1997.
Publication Statements
- Publisher(s):Birkhäuser Verlag
- Place of Publication:Basel
- Language:eng
- Publication Date:©1997.
The Physical Object
- Description:1 online resource (xi, 212 pages)
Edition Identifiers
- ISBN:9783034888868, 3034888864
- oclc:ocn812613013
- LC Classification:QA315
- Dewey Decimal:515/.64
Table of Contents
1. Introduction -- 2. Some Variational Problems -- 3. The Calculus of Variations under Convexity Assumptions -- 4. Nonconvexity and Relaxation -- 5. Phase Transitions and Microstructure -- 6. Parametrized Measures -- 7 Analysis of Parametrized Measures -- 8. Analysis of Gradient Parametrized Measures -- 9. Quasiconvexity and Rank-one Convexity -- 10. Analysis of Divergence-Free Parametrized Measures.
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