Calculus of Variations and Partial Differential Equations

Topics on Geometrical Evolution Problems and Degree Theory

Author: Luigi Ambrosio,Norman Dancer

Publisher: Springer Science & Business Media

ISBN: 3642571867

Category: Mathematics

Page: 348

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At the summer school in Pisa in September 1996, Luigi Ambrosio and Norman Dancer each gave a course on the geometric problem of evolution of a surface by mean curvature, and degree theory with applications to PDEs respectively. This self-contained presentation accessible to PhD students bridged the gap between standard courses and advanced research on these topics. The resulting book is divided accordingly into 2 parts, and neatly illustrates the 2-way interaction of problems and methods. Each of the courses is augmented and complemented by additional short chapters by other authors describing current research problems and results.

Calculus of Variations and Differential Equations

Author: Alexander Ioffe,Simeon Reich,I Shafrir

Publisher: CRC Press

ISBN: 9780849306051

Category: Mathematics

Page: 272

View: 7757

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The calculus of variations is a classical area of mathematical analysis-300 years old-yet its myriad applications in science and technology continue to hold great interest and keep it an active area of research. These two volumes contain the refereed proceedings of the international conference on Calculus of Variations and Related Topics held at the Technion-Israel Institute of Technology in March 1998. The conference commemorated 300 years of work in the field and brought together many of its leading experts. The papers in the first volume focus on critical point theory and differential equations. The other volume deals with variational aspects of optimal control. Together they provide a unique opportunity to review the state-of-the-art of the calculus of variations, as presented by an international panel of masters in the field.

Differential Equations and the Calculus of Variations

Author: Lev Elsgolts

Publisher: N.A

ISBN: 9781410210678

Category: Mathematics

Page: 444

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Originally published in the Soviet Union, this text is meant for students of higher schools and deals with the most important sections of mathematics - differential equations and the calculus of variations. The first part describes the theory of differential equations and reviews the methods for integrating these equations and investigating their solutions. The second part gives an idea of the calculus of variations and surveys the methods for solving variational problems. The book contains a large number of examples and problems with solutions involving applications of mathematics to physics and mechanics. Apart from its main purpose the textbook is of interest to expert mathematicians. Lev Elsgolts (deceased) was a Doctor of Physico-Mathematical Sciences, Professor at the Patrice Lumumba University of Friendship of Peoples. His research work was dedicated to the calculus of variations and differential equations. He worked out the theory of differential equations with deviating arguments and supplied methods for their solution. Lev Elsgolts was the author of many printed works. Among others, he wrote the well-known books Qualitative Methods in Mathematical Analysis and Introduction to the Theory of Differential Equations with Deviating Arguments. In addition to his research work Lev Elsgolts taught at higher schools for over twenty years.

Ordinary Differential Equations and Calculus of Variations

Author: M V Makarets,V Yu Reshetnyak

Publisher: World Scientific

ISBN: 9814500763

Category: Mathematics

Page: 384

View: 1051

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This problem book contains exercises for courses in differential equations and calculus of variations at universities and technical institutes. It is designed for non-mathematics students and also for scientists and practicing engineers who feel a need to refresh their knowledge. The book contains more than 260 examples and about 1400 problems to be solved by the students — much of which have been composed by the authors themselves. Numerous references are given at the end of the book to furnish sources for detailed theoretical approaches, and expanded treatment of applications. Contents:First Order Differential EquationsN-th Order Differential EquationsLinear Second Order EquationsSystems of Differential EquationsPartial Equations of the First OrderNonlinear Equations and StabilityCalculus of VariationsAnswers to Problems Readership: Mathematicians and engineers. keywords:Examples;Differential Equations;Calculus of Variations “… the book can be successfully used both by students and practising engineers.” Mathematics Abstracts

Partial Differential Equations and Calculus of Variations

Author: Stefan Hildebrandt,Rolf Leis

Publisher: Springer

ISBN: 3540460241

Category: Mathematics

Page: 428

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This volume contains 18 invited papers by members and guests of the former Sonderforschungsbereich in Bonn (SFB 72) who, over the years, collaborated on the research group "Solution of PDE's and Calculus of Variations". The emphasis is on existence and regularity results, on special equations of mathematical physics and on scattering theory.

Calculus of Variations and Optimal Control/Differential Equations Set

Author: Alexander Ioffe,Simeon Reich,I Shafrir

Publisher: CRC Press

ISBN: 1584881402

Category: Mathematics

Page: 280

View: 6159

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The calculus of variations is a classical area of mathematical analysis yet its myriad applications in science and technology continue to keep it an active area of research. Encompassing two volumes, this set brings together leading experts who focus on critical point theory, differential equations, and the variational aspects of optimal control. The books cover monotonicity, nonlinear optimization, the impossible pilot wave, the Lavrentiev phenomenon, and elliptic problems.

Calculus of Variations and Nonlinear Partial Differential Equations

Lectures Given at the C.I.M.E. Summer School Held in Cetraro, Italy, June 27 - July 2, 2005

Author: Centro internazionale matematico estivo. Summer School,Luigi Ambrosio,Luis A. Caffarelli,Michael G. Crandall,Lawrence C. Evans,Nicola Fusco

Publisher: Springer Science & Business Media

ISBN: 3540759131

Category: Mathematics

Page: 196

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With a historical overview by Elvira Mascolo

Calculus of Variations and Partial Differential Equations of the First Order

Author: Constantin Carathéodory

Publisher: Courier Corporation

ISBN: 9780821819999

Category: Mathematics

Page: 402

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From the Preface: The book consists of two parts. In the first part, I have made an attempt to simplify the presentation of the theory of partial differential equations to the first order so that its study will require little time and also be accessible to the average student of mathematics ... The second part, which contains the Calculus of Variations, can also be read independently if one refers back to earlier sections in Part I ... I have never lost sight of the fact that the Calculus of Variations, as it is presented in Part II, should above all be a servant of Mechanics. Therefore, I have in particular prepared everything from the very outset for treatment in multidimensional spaces. In this second English edition of Caratheodory's famous work, the two volumes of the first edition have been combined into one (with a combination of the two indexes into a single index). There is a deep and fundamental relationship between the differential equations that occur in the calculus of variations and partial differential equations of the first order: in particular, to each such partial differential equation there correspond variational problems. This basic fact forms the rationale for Caratheodory's masterpiece.

Partielle Differentialgleichungen der Geometrie und der Physik 2

Funktionalanalytische Lösungsmethoden

Author: Friedrich Sauvigny

Publisher: Springer-Verlag

ISBN: 3540275401

Category: Mathematics

Page: 350

View: 530

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Das zweibändige Lehrbuch behandelt das Gebiet der partiellen Differentialgleichungen umfassend und anschaulich. Der Autor stellt in Band 2 funktionalanalytische Lösungsmethoden vor und erläutert u. a. die Lösbarkeit von Operatorgleichungen im Banachraum, lineare Operatoren im Hilbertraum und Spektraltheorie, die Schaudersche Theorie linearer elliptischer Differentialgleichungen sowie schwache Lösungen elliptischer Differentialgleichungen.

The Inverse Problem of the Calculus of Variations for Ordinary Differential Equations

Author: Ian Anderson,Gerard Thompson

Publisher: American Mathematical Soc.

ISBN: 9780821861967

Category: Mathematics

Page: 110

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This monograph explores various aspects of the inverse problem of the calculus of variations for systems of ordinary differential equations. The main problem centres on determining the existence and degree of generality of Lagrangians whose system of Euler-Lagrange equations coicides with a given system of ordinary differential equations. The authors rederive the basic necessary and sufficient conditions of Douglas for second order equations and extend them to equations of higher order using methods of the variational bicomplex of Tulcyjew, Vinogradov, and Tsujishita. The authors present an algorithm, based upon exterior differential systems techniques, for solving the inverse problem for second order equations. a number of new examples illustrate the effectiveness of this approach.

Direct Methods in the Calculus of Variations

Author: Enrico Giusti

Publisher: World Scientific

ISBN: 9814488291

Category: Mathematics

Page: 412

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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. Contents:Semi-Classical TheoryMeasurable FunctionsSobolev SpacesConvexity and SemicontinuityQuasi-Convex FunctionalsQuasi-MinimaHölder ContinuityFirst DerivativesPartial RegularityHigher Derivatives Readership: Graduate students, academics and researchers in the field of analysis and differential equations. Keywords:Reviews:“This book must be recommended both to beginners in variational calculus and to more confirmed specialists in regularity theory of elliptic problems. It will become a reference in the calculus of variations and it contains in one volume of a reasonable size a very clear presentation of deep results.”Zentralblatt MATH “It can be recommended for graduate courses or post-graduate courses in the calculus of variations, or as reference text.”Studia Universitatis Babes-Bolyai, Series Mathematica “The exposition is always clear and self-contained … therefore this book may serve well as a textbook for a graduate course on the subject. Each chapter is complemented with detailed historical notes and interesting results which may be difficult to find elsewhere.”Mathematical Reviews

Introduction to the Calculus of Variations

Author: U. Brechteken-Mandersch

Publisher: CRC Press

ISBN: 9780412366901

Category: Mathematics

Page: 208

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This text provides a clear, concise introduction to the calculus of variations. The introductory chapter provides a general sense of the subject through a discussion of several classical and contemporary examples of the subject's use.

Introduction to the Calculus of Variations

Author: Hans Sagan

Publisher: Courier Corporation

ISBN: 048613802X

Category: Mathematics

Page: 480

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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.

Calculus of Variations

With Applications to Physics and Engineering

Author: Robert Weinstock

Publisher: Courier Corporation

ISBN: 9780486630694

Category: Mathematics

Page: 326

View: 5689

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This text is basically divided into two parts. Chapters 1–4 include background material, basic theorems and isoperimetric problems. Chapters 5–12 are devoted to applications, geometrical optics, particle dynamics, the theory of elasticity, electrostatics, quantum mechanics, and other topics. Exercises in each chapter. 1952 edition.

Calculus of Variations I

Author: Mariano Giaquinta,Stefan Hildebrandt

Publisher: Springer Science & Business Media

ISBN: 9783540506256

Category: Mathematics

Page: 474

View: 7196

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This two-volume treatise is a standard reference in the field. It pays special attention to the historical aspects and the origins partly in applied problems—such as those of geometric optics—of parts of the theory. It contains an introduction to each chapter, section, and subsection and an overview of the relevant literature in the footnotes and bibliography. It also includes an index of the examples used throughout the book.

Introduction To The Calculus of Variations And Its Applications, Second Edition

Author: Frederic Wan

Publisher: CRC Press

ISBN: 9780412051418

Category: Mathematics

Page: 640

View: 2104

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This comprehensive text provides all information necessary for an introductory course on the calculus of variations and optimal control theory. Following a thorough discussion of the basic problem, including sufficient conditions for optimality, the theory and techniques are extended to problems with a free end point, a free boundary, auxiliary and inequality constraints, leading to a study of optimal control theory.

An Introduction to the Calculus of Variations

Author: Charles Fox

Publisher: Courier Corporation

ISBN: 9780486654997

Category: Mathematics

Page: 271

View: 7639

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In this highly regarded text for advanced undergraduate and graduate students, the author develops the calculus of variations both for its intrinsic interest and for its powerful applications to modern mathematical physics. Topics include first and second variations of an integral, generalizations, isoperimetrical problems, least action, special relativity, elasticity, more. 1963 edition.