One Dimensional Variational Problems

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One-dimensional Variational Problems

Giuseppe Buttazzo,Mariano Giaquinta,Stefan Hildebrandt
One dimensional Variational Problems Book PDF

Author : Giuseppe Buttazzo,Mariano Giaquinta,Stefan Hildebrandt
Publisher : Oxford University Press
Page : 282 pages
File Size : 50,7 Mb
Release : 1998
Category : Mathematics
ISBN : 0198504659

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One-dimensional Variational Problems by Giuseppe Buttazzo,Mariano Giaquinta,Stefan Hildebrandt Pdf

While easier to solve and accessible to a broader range of students, one-dimensional variational problems and their associated differential equations exhibit many of the same complex behavior of higher-dimensional problems. This book, the first moden introduction, emphasizes direct methods and provides an exceptionally clear view of the underlying theory.

Branching Solutions to One-dimensional Variational Problems

Alexander O. Ivanov,A. A. Tuzhilin
Branching Solutions to One dimensional Variational Problems Book PDF

Author : Alexander O. Ivanov,A. A. Tuzhilin
Publisher : World Scientific
Page : 365 pages
File Size : 47,8 Mb
Release : 2001
Category : Mathematics
ISBN : 9789812810717

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Branching Solutions to One-dimensional Variational Problems by Alexander O. Ivanov,A. A. Tuzhilin Pdf

This book deals with the new class of one-dimensional variational problems OCo the problems with branching solutions. Instead of extreme curves (mappings of a segment to a manifold) we investigate extreme networks, which are mappings of graphs (one-dimensional cell complexes) to a manifold. Various applications of the approach are presented, such as several generalizations of the famous Steiner problem of finding the shortest network spanning given points of the plane. Contents: Preliminary Results; Networks Extremality Criteria; Linear Networks in R N; Extremals of Length Type Functionals: The Case of Parametric Networks; Extremals of Functionals Generated by Norms. Readership: Researchers in differential geometry and topology."

Calculus of Variations

Hansjörg Kielhöfer
Calculus of Variations Book PDF

Author : Hansjörg Kielhöfer
Publisher : Springer
Page : 227 pages
File Size : 50,9 Mb
Release : 2018-01-25
Category : Mathematics
ISBN : 9783319711232

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Calculus of Variations by Hansjörg Kielhöfer Pdf

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.

Branching Solutions to One-dimensional Variational Problems

Alexander O. Ivanov,A. A. Tuzhilin
Branching Solutions to One dimensional Variational Problems Book PDF

Author : Alexander O. Ivanov,A. A. Tuzhilin
Publisher : World Scientific
Page : 365 pages
File Size : 48,8 Mb
Release : 2001
Category : Mathematics
ISBN : 9789810240608

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Branching Solutions to One-dimensional Variational Problems by Alexander O. Ivanov,A. A. Tuzhilin Pdf

This study deals with the new class of one-dimensional variational problems - the problems with branching solutions. Instead of extreme curves (mappings of a segment to a manifold) it investigates extreme networks, which are mappings of graphs (one-dimensional cell complexes) to a manifold. Various applications of the approach are presented, such as several generalizations of the famous Steiner problem of finding the shortest network spanning given points of the plane.

Variational Methods for Structural Optimization

Andrej Cherkaev
Variational Methods for Structural Optimization Book PDF

Author : Andrej Cherkaev
Publisher : Springer Science & Business Media
Page : 561 pages
File Size : 41,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461211884

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Variational Methods for Structural Optimization by Andrej Cherkaev Pdf

This book bridges a gap between a rigorous mathematical approach to variational problems and the practical use of algorithms of structural optimization in engineering applications. The foundations of structural optimization are presented in sufficiently simple form as to make them available for practical use.

Geometrical Methods in Variational Problems

N.A. Bobylov,S.V. Emel'yanov,S. Korovin
Geometrical Methods in Variational Problems Book PDF

Author : N.A. Bobylov,S.V. Emel'yanov,S. Korovin
Publisher : Springer Science & Business Media
Page : 556 pages
File Size : 43,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401146296

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Geometrical Methods in Variational Problems by N.A. Bobylov,S.V. Emel'yanov,S. Korovin Pdf

This self-contained monograph presents methods for the investigation of nonlinear variational problems. These methods are based on geometric and topological ideas such as topological index, degree of a mapping, Morse-Conley index, Euler characteristics, deformation invariant, homotopic invariant, and the Lusternik-Shnirelman category. Attention is also given to applications in optimisation, mathematical physics, control, and numerical methods. Audience: This volume will be of interest to specialists in functional analysis and its applications, and can also be recommended as a text for graduate and postgraduate-level courses in these fields.

Recent Developments in Well-Posed Variational Problems

Roberto Lucchetti,Julian Revalski
Recent Developments in Well Posed Variational Problems Book PDF

Author : Roberto Lucchetti,Julian Revalski
Publisher : Springer Science & Business Media
Page : 271 pages
File Size : 41,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401584722

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Recent Developments in Well-Posed Variational Problems by Roberto Lucchetti,Julian Revalski Pdf

This volume contains several surveys focused on the ideas of approximate solutions, well-posedness and stability of problems in scalar and vector optimization, game theory and calculus of variations. These concepts are of particular interest in many fields of mathematics. The idea of stability goes back at least to J. Hadamard who introduced it in the setting of differential equations; the concept of well-posedness for minimum problems is more recent (the mid-sixties) and originates with A.N. Tykhonov. It turns out that there are connections between the two properties in the sense that a well-posed problem which, at least in principle, is "easy to solve", has a solution set that does not vary too much under perturbation of the data of the problem, i.e. it is "stable". These themes have been studied in depth for minimum problems and now we have a general picture of the related phenomena in this case. But, of course, the same concepts can be studied in other more complicated situations as, e.g. vector optimization, game theory and variational inequalities. Let us mention that in several of these new areas there is not even a unique idea of what should be called approximate solution, and the latter is at the basis of the definition of well posed problem.

Mechanics and Thermodynamics of Continua

Hershel Markovitz,Victor J. Mizel,David R. Owen
Mechanics and Thermodynamics of Continua Book PDF

Author : Hershel Markovitz,Victor J. Mizel,David R. Owen
Publisher : Springer Science & Business Media
Page : 575 pages
File Size : 43,9 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9783642759758

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Mechanics and Thermodynamics of Continua by Hershel Markovitz,Victor J. Mizel,David R. Owen Pdf

Reprinted from Archive for Rational Mechanics and Analysis edited by C. Truesdell

Convex Analysis and Variational Problems

Ivar Ekeland,Roger Temam
Convex Analysis and Variational Problems Book PDF

Author : Ivar Ekeland,Roger Temam
Publisher : SIAM
Page : 414 pages
File Size : 41,9 Mb
Release : 1999-12-01
Category : Mathematics
ISBN : 161197108X

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Convex Analysis and Variational Problems by Ivar Ekeland,Roger Temam Pdf

This book contains different developments of infinite dimensional convex programming in the context of convex analysis, including duality, minmax and Lagrangians, and convexification of nonconvex optimization problems in the calculus of variations (infinite dimension). It also includes the theory of convex duality applied to partial differential equations; no other reference presents this in a systematic way. The minmax theorems contained in this book have many useful applications, in particular the robust control of partial differential equations in finite time horizon. First published in English in 1976, this SIAM Classics in Applied Mathematics edition contains the original text along with a new preface and some additional references.

Convex Analysis and Variational Problems

Ivar Ekeland,Roger Temam
Convex Analysis and Variational Problems Book PDF

Author : Ivar Ekeland,Roger Temam
Publisher : SIAM
Page : 405 pages
File Size : 47,7 Mb
Release : 1999-12-01
Category : Mathematics
ISBN : 9780898714500

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Convex Analysis and Variational Problems by Ivar Ekeland,Roger Temam Pdf

No one working in duality should be without a copy of Convex Analysis and Variational Problems. This book contains different developments of infinite dimensional convex programming in the context of convex analysis, including duality, minmax and Lagrangians, and convexification of nonconvex optimization problems in the calculus of variations (infinite dimension). It also includes the theory of convex duality applied to partial differential equations; no other reference presents this in a systematic way. The minmax theorems contained in this book have many useful applications, in particular the robust control of partial differential equations in finite time horizon. First published in English in 1976, this SIAM Classics in Applied Mathematics edition contains the original text along with a new preface and some additional references.

Introduction to Numerical Methods for Variational Problems

Hans Petter Langtangen,Kent-Andre Mardal
Introduction to Numerical Methods for Variational Problems Book PDF

Author : Hans Petter Langtangen,Kent-Andre Mardal
Publisher : Springer Nature
Page : 395 pages
File Size : 51,8 Mb
Release : 2019-09-26
Category : Mathematics
ISBN : 9783030237882

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Introduction to Numerical Methods for Variational Problems by Hans Petter Langtangen,Kent-Andre Mardal Pdf

This textbook teaches finite element methods from a computational point of view. It focuses on how to develop flexible computer programs with Python, a programming language in which a combination of symbolic and numerical tools is used to achieve an explicit and practical derivation of finite element algorithms. The finite element library FEniCS is used throughout the book, but the content is provided in sufficient detail to ensure that students with less mathematical background or mixed programming-language experience will equally benefit. All program examples are available on the Internet.

Variational Problems in Differential Geometry

Roger Bielawski,Kevin Houston,Martin Speight
Variational Problems in Differential Geometry Book PDF

Author : Roger Bielawski,Kevin Houston,Martin Speight
Publisher : Cambridge University Press
Page : 216 pages
File Size : 55,8 Mb
Release : 2011-10-20
Category : Mathematics
ISBN : 9781139504119

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Variational Problems in Differential Geometry by Roger Bielawski,Kevin Houston,Martin Speight Pdf

With a mix of expository and original papers this volume is an excellent reference for experienced researchers in geometric variational problems, as well as an ideal introduction for graduate students. It presents all the varied methods and techniques used in attacking geometric variational problems and includes many up-to-date results.

Two-Dimensional Geometric Variational Problems

Jürgen Jost
Two Dimensional Geometric Variational Problems Book PDF

Author : Jürgen Jost
Publisher : Unknown
Page : 256 pages
File Size : 55,6 Mb
Release : 1991-03-29
Category : Mathematics
ISBN : UOM:39015029249748

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Two-Dimensional Geometric Variational Problems by Jürgen Jost Pdf

This monograph treats variational problems for mappings from a surface equipped with a conformal structure into Euclidean space or a Riemannian manifold. Presents a general theory of such variational problems, proving existence and regularity theorems with particular conceptual emphasis on the geometric aspects of the theory and thorough investigation of the connections with complex analysis. Among the topics covered are: Plateau's problem, the regularity theory of solutions, a variational approach for obtaining various conformal representation theorems, a general existence theorem for harmonic mappings, and a new approach to Teichmuller theory via harmonic maps.

A Course in the Calculus of Variations

Filippo Santambrogio
A Course in the Calculus of Variations Book PDF

Author : Filippo Santambrogio
Publisher : Springer Nature
Page : 354 pages
File Size : 40,9 Mb
Release : 2024-01-18
Category : Mathematics
ISBN : 9783031450365

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A Course in the Calculus of Variations by Filippo Santambrogio Pdf

This book provides an introduction to the broad topic of the calculus of variations. It addresses the most natural questions on variational problems and the mathematical complexities they present. Beginning with the scientific modeling that motivates the subject, the book then tackles mathematical questions such as the existence and uniqueness of solutions, their characterization in terms of partial differential equations, and their regularity. It includes both classical and recent results on one-dimensional variational problems, as well as the adaptation to the multi-dimensional case. Here, convexity plays an important role in establishing semi-continuity results and connections with techniques from optimization, and convex duality is even used to produce regularity results. This is then followed by the more classical Hölder regularity theory for elliptic PDEs and some geometric variational problems on sets, including the isoperimetric inequality and the Steiner tree problem. The book concludes with a chapter on the limits of sequences of variational problems, expressed in terms of Γ-convergence. While primarily designed for master's-level and advanced courses, this textbook, based on its author's instructional experience, also offers original insights that may be of interest to PhD students and researchers. A foundational understanding of measure theory and functional analysis is required, but all the essential concepts are reiterated throughout the book using special memo-boxes.

Nonconvex Optimal Control and Variational Problems

Alexander J. Zaslavski
Nonconvex Optimal Control and Variational Problems Book PDF

Author : Alexander J. Zaslavski
Publisher : Springer Science & Business Media
Page : 382 pages
File Size : 48,5 Mb
Release : 2013-06-12
Category : Mathematics
ISBN : 9781461473787

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Nonconvex Optimal Control and Variational Problems by Alexander J. Zaslavski Pdf

Nonconvex Optimal Control and Variational Problems is an important contribution to the existing literature in the field and is devoted to the presentation of progress made in the last 15 years of research in the area of optimal control and the calculus of variations. This volume contains a number of results concerning well-posedness of optimal control and variational problems, nonoccurrence of the Lavrentiev phenomenon for optimal control and variational problems, and turnpike properties of approximate solutions of variational problems. Chapter 1 contains an introduction as well as examples of select topics. Chapters 2-5 consider the well-posedness condition using fine tools of general topology and porosity. Chapters 6-8 are devoted to the nonoccurrence of the Lavrentiev phenomenon and contain original results. Chapter 9 focuses on infinite-dimensional linear control problems, and Chapter 10 deals with “good” functions and explores new understandings on the questions of optimality and variational problems. Finally, Chapters 11-12 are centered around the turnpike property, a particular area of expertise for the author. This volume is intended for mathematicians, engineers, and scientists interested in the calculus of variations, optimal control, optimization, and applied functional analysis, as well as both undergraduate and graduate students specializing in those areas. The text devoted to Turnpike properties may be of particular interest to the economics community.