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Author: Irene Fonseca
Publisher: Springer Science & Business Media
ISBN: 0387690069
Category : Science
Languages : en
Pages : 602
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Book Description
This is the first of two books on methods and techniques in the calculus of variations. Contemporary arguments are used throughout the text to streamline and present in a unified way classical results, and to provide novel contributions at the forefront of the theory. This book addresses fundamental questions related to lower semicontinuity and relaxation of functionals within the unconstrained setting, mainly in L^p spaces. It prepares the ground for the second volume where the variational treatment of functionals involving fields and their derivatives will be undertaken within the framework of Sobolev spaces. This book is self-contained. All the statements are fully justified and proved, with the exception of basic results in measure theory, which may be found in any good textbook on the subject. It also contains several exercises. Therefore,it may be used both as a graduate textbook as well as a reference text for researchers in the field. Irene Fonseca is the Mellon College of Science Professor of Mathematics and is currently the Director of the Center for Nonlinear Analysis in the Department of Mathematical Sciences at Carnegie Mellon University. Her research interests lie in the areas of continuum mechanics, calculus of variations, geometric measure theory and partial differential equations. Giovanni Leoni is also a professor in the Department of Mathematical Sciences at Carnegie Mellon University. He focuses his research on calculus of variations, partial differential equations and geometric measure theory with special emphasis on applications to problems in continuum mechanics and in materials science.
Author: Irene Fonseca
Publisher: Springer Science & Business Media
ISBN: 0387690069
Category : Science
Languages : en
Pages : 602
Get Book
Book Description
This is the first of two books on methods and techniques in the calculus of variations. Contemporary arguments are used throughout the text to streamline and present in a unified way classical results, and to provide novel contributions at the forefront of the theory. This book addresses fundamental questions related to lower semicontinuity and relaxation of functionals within the unconstrained setting, mainly in L^p spaces. It prepares the ground for the second volume where the variational treatment of functionals involving fields and their derivatives will be undertaken within the framework of Sobolev spaces. This book is self-contained. All the statements are fully justified and proved, with the exception of basic results in measure theory, which may be found in any good textbook on the subject. It also contains several exercises. Therefore,it may be used both as a graduate textbook as well as a reference text for researchers in the field. Irene Fonseca is the Mellon College of Science Professor of Mathematics and is currently the Director of the Center for Nonlinear Analysis in the Department of Mathematical Sciences at Carnegie Mellon University. Her research interests lie in the areas of continuum mechanics, calculus of variations, geometric measure theory and partial differential equations. Giovanni Leoni is also a professor in the Department of Mathematical Sciences at Carnegie Mellon University. He focuses his research on calculus of variations, partial differential equations and geometric measure theory with special emphasis on applications to problems in continuum mechanics and in materials science.
Author: Irene Fonseca
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Author: I. M. Gelfand
Publisher: Courier Corporation
ISBN: 0486135012
Category : Mathematics
Languages : en
Pages : 240
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Book Description
Fresh, lively text serves as a modern introduction to the subject, with applications to the mechanics of systems with a finite number of degrees of freedom. Ideal for math and physics students.
Author: Hans Sagan
Publisher: Courier Corporation
ISBN: 048613802X
Category : Mathematics
Languages : en
Pages : 484
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Book Description
Provides a thorough understanding of calculus of variations and prepares readers for the study of modern optimal control theory. Selected variational problems and over 400 exercises. Bibliography. 1969 edition.
Author: Hansjörg Kielhöfer
Publisher: Springer
ISBN: 3319711237
Category : Mathematics
Languages : en
Pages : 227
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Book Description
This clear and concise textbook provides a rigorous introduction to the calculus of variations, depending on functions of one variable and their first derivatives. It is based on a translation of a German edition of the book Variationsrechnung (Vieweg+Teubner Verlag, 2010), translated and updated by the author himself. Topics include: the Euler-Lagrange equation for one-dimensional variational problems, with and without constraints, as well as an introduction to the direct methods. The book targets students who have a solid background in calculus and linear algebra, not necessarily in functional analysis. Some advanced mathematical tools, possibly not familiar to the reader, are given along with proofs in the appendix. Numerous figures, advanced problems and proofs, examples, and exercises with solutions accompany the book, making it suitable for self-study. The book will be particularly useful for beginning graduate students from the physical, engineering, and mathematical sciences with a rigorous theoretical background.
Author: Robert Weinstock
Publisher: Courier Corporation
ISBN: 0486141063
Category : Mathematics
Languages : en
Pages : 354
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Book Description
This book by Robert Weinstock was written to fill the need for a basic introduction to the calculus of variations. Simply and easily written, with an emphasis on the applications of this calculus, it has long been a standard reference of physicists, engineers, and applied mathematicians. The author begins slowly, introducing the reader to the calculus of variations, and supplying lists of essential formulae and derivations. Later chapters cover isoperimetric problems, geometrical optics, Fermat's principle, dynamics of particles, the Sturm-Liouville eigenvalue-eigenfunction problem, the theory of elasticity, quantum mechanics, and electrostatics. Each chapter ends with a series of exercises which should prove very useful in determining whether the material in that chapter has been thoroughly grasped. The clarity of exposition makes this book easily accessible to anyone who has mastered first-year calculus with some exposure to ordinary differential equations. Physicists and engineers who find variational methods evasive at times will find this book particularly helpful. "I regard this as a very useful book which I shall refer to frequently in the future." J. L. Synge, Bulletin of the American Mathematical Society.
Author: Mike Mesterton-Gibbons
Publisher: American Mathematical Soc.
ISBN: 0821847724
Category : Mathematics
Languages : en
Pages : 274
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Book Description
The calculus of variations is used to find functions that optimize quantities expressed in terms of integrals. Optimal control theory seeks to find functions that minimize cost integrals for systems described by differential equations. This book is an introduction to both the classical theory of the calculus of variations and the more modern developments of optimal control theory from the perspective of an applied mathematician. It focuses on understanding concepts and how to apply them. The range of potential applications is broad: the calculus of variations and optimal control theory have been widely used in numerous ways in biology, criminology, economics, engineering, finance, management science, and physics. Applications described in this book include cancer chemotherapy, navigational control, and renewable resource harvesting. The prerequisites for the book are modest: the standard calculus sequence, a first course on ordinary differential equations, and some facility with the use of mathematical software. It is suitable for an undergraduate or beginning graduate course, or for self study. It provides excellent preparation for more advanced books and courses on the calculus of variations and optimal control theory.
Author: Jürgen Jost
Publisher: Cambridge University Press
ISBN: 9780521642033
Category : Mathematics
Languages : en
Pages : 348
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Book Description
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Author: Michael Struwe
Publisher: Springer Science & Business Media
ISBN: 3662032120
Category : Science
Languages : en
Pages : 288
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Book Description
Hilbert's talk at the second International Congress of 1900 in Paris marked the beginning of a new era in the calculus of variations. A development began which, within a few decades, brought tremendous success, highlighted by the 1929 theorem of Ljusternik and Schnirelman on the existence of three distinct prime closed geodesics on any compact surface of genus zero, and the 1930/31 solution of Plateau's problem by Douglas and Radò. The book gives a concise introduction to variational methods and presents an overview of areas of current research in this field. This new edition has been substantially enlarged, a new chapter on the Yamabe problem has been added and the references have been updated. All topics are illustrated by carefully chosen examples, representing the current state of the art in their field.
Author: Enrico Giusti
Publisher: World Scientific
ISBN: 9812380434
Category : Mathematics
Languages : en
Pages : 412
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Book Description
This book provides a comprehensive discussion on the existence and regularity of minima of regular integrals in the calculus of variations and of solutions to elliptic partial differential equations and systems of the second order. While direct methods for the existence of solutions are well known and have been widely used in the last century, the regularity of the minima was always obtained by means of the Euler equation as a part of the general theory of partial differential equations. In this book, using the notion of the quasi-minimum introduced by Giaquinta and the author, the direct methods are extended to the regularity of the minima of functionals in the calculus of variations, and of solutions to partial differential equations. This unified treatment offers a substantial economy in the assumptions, and permits a deeper understanding of the nature of the regularity and singularities of the solutions. The book is essentially self-contained, and requires only a general knowledge of the elements of Lebesgue integration theory.
