This book is developed for the study of vectorial problems in the calculus of variations. The subject is a very active one and almost half of the book consists of new material. This is a new edition of the earlier book published in 1989 and it is suitable for graduate students. The book has been updated with some new material and examples added. Applications are included.
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Editorial Reviews
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From the reviews of the second edition:
"This new edition is very much expanded, up to the point that it can be considered an almost entirely new book. … I was a PhD student in the early 90’s, and I have been studying and using it continuously since then. It has accompanied me and many others as a valuable source for results and as a standard reference on the subject. I am sure that this new edition will be serving in the same role as well." (Pietro Celada, Mathematical Reviews, Issue 2008 m)
"The present monograph has been … a ‘revised and augmented edition to Direct Methods in the Calculus of Variations’. … the author maintains a fresh and lucid style, resulting in a concise, very well readable presentation. Surely this book will define a long-lasting standard in its area. … The exhaustive bibliography comprises 621 references and covers the relevant publications in the area … ." (Marcus Wagner, Zentralblatt MATH, Vol. 1140, 2008)
From the Back Cover
This book studies vectorial problems in the calculus of variations and quasiconvex analysis. It is a new edition of the earlier book published in 1989 and has been updated with some new material and examples added.
This monograph will appeal to researchers and graduate students in mathematics and engineering.
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Inside This Book
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Key Phrases - Statistically Improbable Phrases (SIPs):
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weak continuity, rank one convex sets, rank one convex functions, one convex sense, separately convex sense, signed singular values, relaxation property with respect, underdetermined partial differential equations, one convex envelopes, rank one affine, polyconvex sense, rank one convex hulls, polyconvex set, rank one convexity, polyconvex functions, quasiaffine function, vectorial case, rank one direction, relaxation theorems, polyconvex envelope, quasiconvex analysis, proof into two steps, quasiconvex envelope, rank one convex envelope, quasiconvex case Key Phrases - Capitalized Phrases (CAPs): (learn more)
Extension of Lipschitz, Using Theorem, Applying Theorem, Using Hölder, Using Proposition, Saint Venant-Kirchhoff, Von Wahl, Applying Step Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
weak continuity, rank one convex sets, rank one convex functions, one convex sense, separately convex sense, signed singular values, relaxation property with respect, underdetermined partial differential equations, one convex envelopes, rank one affine, polyconvex sense, rank one convex hulls, polyconvex set, rank one convexity, polyconvex functions, quasiaffine function, vectorial case, rank one direction, relaxation theorems, polyconvex envelope, quasiconvex analysis, proof into two steps, quasiconvex envelope, rank one convex envelope, quasiconvex case Key Phrases - Capitalized Phrases (CAPs): (learn more)
Extension of Lipschitz, Using Theorem, Applying Theorem, Using Hölder, Using Proposition, Saint Venant-Kirchhoff, Von Wahl, Applying Step Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
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