Book Description

Over the last few decades, research in elastic-plastic torsion theory, electrostatic screening, and rubber-like nonlinear elastomers has pointed the way to some interesting new classes of minimum problems for energy functionals of the calculus of variations. This advanced-level monograph addresses these issues by developing the framework of a general theory of integral representation, relaxation, and homogenization for unbounded functionals. The first part of the book builds the foundation for the general theory with concepts and tools from convex analysis, measure theory, and the theory of variational convergences. The authors then introduce some function spaces and explore some lower semicontinuity and minimization problems for energy functionals. Next, they survey some specific aspects the theory of standard functionals.The second half of the book carefully develops a theory of unbounded, translation invariant functionals that leads to results deeper than those already known, including unique extension properties, representation as integrals of the calculus of variations, relaxation theory, and homogenization processes. In this study, some new phenomena are pointed out. The authors' approach is unified and elegant, the text well written, and the results intriguing and useful, not just in various fields of mathematics, but also in a range of applied mathematics, physics, and material science disciplines. ... Read more

Book Description

Using the same innovative and proven approach that made the authors’ Engineering Mathematics a worldwide bestseller, this book can be used in the classroom or as an in-depth self-study guide. Its unique programmed approach patiently presents the mathematics in a step-by-step fashion together with a wealth of worked examples and exercises. It also contains Quizzes, Learning Outcomes, and Can You? checklists that guide readers through each topic and reinforce learning and comprehension. Both students and professionals alike will find this book a very effective learning tool and reference.

Distinctive Features

- Uses a unique programmed approach that takes readers through the mathematics in a step-by-step fashion with a wealth of worked examples and exercises.
- Contains many Quizzes, Learning Outcomes, and Can You? checklists.
- Ideal as a classroom textbook or a self-learning manual. ... Read more

Reviews (1)

special literature?!-here it is!
It was the first book to disscus the inverse spectral Sturm-Liouville problem with boudary value conditions for a=b=0.Unlike the other books in the field they give the full representation of izospectral set making results more noticeable. Actually it is wonderfull how they introduce the material, it's like a thing Hilbert used to do-siplicity of definitions and as a result simplicity of theory.

P.S. I was looking for this book for too long period of time, first I found out about its existance from the bibliograohy to Trubovitz' article "Invere Sturm-Liouville problem". It was marked: to appear and then I started my search for this book, but to find a special literature in English in Armenia is not to easy a thing. Now I found it and I just love it, not a right word-I need it! ... Read more

Book Description