# Search Results for "direct-methods-in-the-calculus-of-variations-applied-mathematical-sciences"

## Direct Methods in the Calculus of Variations

**Author**: Bernard Dacorogna**Publisher:**Springer Science & Business Media**ISBN:**3642514405**Category:**Mathematics**Page:**308**View:**4401

In recent years there has been a considerable renewal of interest in the clas sical problems of the calculus of variations, both from the point of view of mathematics and of applications. Some of the most powerful tools for proving existence of minima for such problems are known as direct methods. They are often the only available ones, particularly for vectorial problems. It is the aim of this book to present them. These methods were introduced by Tonelli, following earlier work of Hilbert and Lebesgue. Although there are excellent books on calculus of variations and on direct methods, there are recent important developments which cannot be found in these books; in particular, those dealing with vector valued functions and relaxation of non convex problems. These two last ones are important in appli cations to nonlinear elasticity, optimal design . . . . In these fields the variational methods are particularly effective. Part of the mathematical developments and of the renewal of interest in these methods finds its motivations in nonlinear elasticity. Moreover, one of the recent important contributions to nonlinear analysis has been the study of the behaviour of nonlinear functionals un der various types of convergence, particularly the weak convergence. Two well studied theories have now been developed, namely f-convergence and compen sated compactness. They both include as a particular case the direct methods of the calculus of variations, but they are also, both, inspired and have as main examples these direct methods.

## Modern Methods in the Calculus of Variations

*L^p Spaces*

**Author**: Irene Fonseca,Giovanni Leoni**Publisher:**Springer Science & Business Media**ISBN:**0387690069**Category:**Science**Page:**600**View:**9937

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.

## Partielle Differentialgleichungen

*Eine anwendungsorientierte Einführung*

**Author**: Ben Schweizer**Publisher:**Springer-Verlag**ISBN:**3662566680**Category:**Mathematics**Page:**585**View:**3628

Das Buch führt in die Theorie der Partiellen Differentialgleichungen ein, lediglich die Grundvorlesungen der Analysis werden vorausgesetzt. Eine Vielzahl linearer und nichtlinearer Differentialgleichungen wird mit Modellierungsansätzen motiviert und rigoros analysiert. Nach den klassischen linearen Problemen der Potentialtheorie und Wärmeleitung werden insbesondere nichtlineare Probleme aus der Theorie poröser Medien, der Strömungsmechanik und der Festkörpermechanik behandelt. Entlang der Aufgabenstellungen von zunehmender Komplexität werden moderne Methoden und Theorien der Analysis entwickelt. In der vorliegenden 2. Auflage ist der Text überarbeitet und korrigiert, viele Zeichnungen sind verbessert, Anhang und Index sind erweitert.

## Multifield Problems

*State of the Art*

**Author**: Anna-Margarete Sändig,W. Schiehlen,W.L. Wendland**Publisher:**Springer Science & Business Media**ISBN:**9783540675112**Category:**Technology & Engineering**Page:**278**View:**884

The simulation of complex engineering problems often involves an interaction or coupling of individual phenomena, which are traditionally related by themselves to separate fields of applied mechanics. Typical examples of these so- called multifield problems are the thermo-mechanical analysis of solids with coupling between mechanical stress analysis and thermal heat transfer processes, the simulation of coupled deformation and fluid transport mechanisms in porous media, the prediction of mass transport and phase transition phenomena of mixtures, the analysis of sedimentation proces- ses based on an interaction of particle dynamics and viscous flow, the simulation of multibody systems and fluid-structure interactions based on solid-to-solid and solid-to-fluid contact mechanisms.

## Progress in Partial Differential Equations

*The Metz Surveys 4*

**Author**: Michel Chipot,I Shafrir**Publisher:**CRC Press**ISBN:**9780582277304**Category:**Mathematics**Page:**248**View:**1341

This Research Note presents some recent advances in various important domains of partial differential equations and applied mathematics, in particular for calculus of variations and fluid flows. These topics are now part of various areas of science and have experienced tremendous development during the last decades.

## Special issue, current and future challenges in the applications of mathematics

**Author**: Brown University. Division of Applied Mathematics**Publisher:**N.A**ISBN:**N.A**Category:**Education**Page:**220**View:**9089

## Applied Mathematical Methods in Theoretical Physics

**Author**: Michio Masujima**Publisher:**John Wiley & Sons**ISBN:**3527604901**Category:**Science**Page:**11**View:**6290

All there is to know about functional analysis, integral equations and calculus of variations in a single volume. This advanced textbook is divided into two parts: The first on integral equations and the second on the calculus of variations. It begins with a short introduction to functional analysis, including a short review of complex analysis, before continuing a systematic discussion of different types of equations, such as Volterra integral equations, singular integral equations of Cauchy type, integral equations of the Fredholm type, with a special emphasis on Wiener-Hopf integral equations and Wiener-Hopf sum equations. After a few remarks on the historical development, the second part starts with an introduction to the calculus of variations and the relationship between integral equations and applications of the calculus of variations. It further covers applications of the calculus of variations developed in the second half of the 20th century in the fields of quantum mechanics, quantum statistical mechanics and quantum field theory. Throughout the book, the author presents over 150 problems and exercises - many from such branches of physics as quantum mechanics, quantum statistical mechanics, and quantum field theory - together with outlines of the solutions in each case. Detailed solutions are given, supplementing the materials discussed in the main text, allowing problems to be solved making direct use of the method illustrated. The original references are given for difficult problems. The result is complete coverage of the mathematical tools and techniques used by physicists and applied mathematicians Intended for senior undergraduates and first-year graduates in science and engineering, this is equally useful as a reference and self-study guide.

## Advanced Methods in the Fractional Calculus of Variations

**Author**: Agnieszka B. Malinowska,Tatiana Odzijewicz,Delfim F.M. Torres**Publisher:**Springer**ISBN:**3319147560**Category:**Mathematics**Page:**135**View:**7394

This brief presents a general unifying perspective on the fractional calculus. It brings together results of several recent approaches in generalizing the least action principle and the Euler–Lagrange equations to include fractional derivatives. The dependence of Lagrangians on generalized fractional operators as well as on classical derivatives is considered along with still more general problems in which integer-order integrals are replaced by fractional integrals. General theorems are obtained for several types of variational problems for which recent results developed in the literature can be obtained as special cases. In particular, the authors offer necessary optimality conditions of Euler–Lagrange type for the fundamental and isoperimetric problems, transversality conditions, and Noether symmetry theorems. The existence of solutions is demonstrated under Tonelli type conditions. The results are used to prove the existence of eigenvalues and corresponding orthogonal eigenfunctions of fractional Sturm–Liouville problems. Advanced Methods in the Fractional Calculus of Variations is a self-contained text which will be useful for graduate students wishing to learn about fractional-order systems. The detailed explanations will interest researchers with backgrounds in applied mathematics, control and optimization as well as in certain areas of physics and engineering.

## Diffusionsmodelle zur geomorphologischen Generalisierung und ihre Finite-Elemente- Diskretisierung

**Author**: Jens Vogelgesang**Publisher:**N.A**ISBN:**N.A**Category:**Geomorphology**Page:**80**View:**2947

## Proceedings of the Workshop "New Developments in the Calculus of Variations"

**Author**: N.A**Publisher:**N.A**ISBN:**9788849513592**Category:**Business & Economics**Page:**154**View:**8993

## Advances in Mathematical Sciences and Applications

**Author**: N.A**Publisher:**N.A**ISBN:**N.A**Category:**Mathematical analysis**Page:**N.A**View:**6007

## Variational Methods in Mathematical Physics

*A Unified Approach*

**Author**: Philippe Blanchard,Erwin Brüning**Publisher:**Springer Science & Business Media**ISBN:**3642826989**Category:**Science**Page:**410**View:**9687

The first edition (in German) had the prevailing character of a textbook owing to the choice of material and the manner of its presentation. This second (translated, revised, and extended) edition, however, includes in its new parts considerably more recent and advanced results and thus goes partially beyond the textbook level. We should emphasize here that the primary intentions of this book are to provide (so far as possible given the restrictions of space) a selfcontained presentation of some modern developments in the direct methods of the cal culus of variations in applied mathematics and mathematical physics from a unified point of view and to link it to the traditional approach. These modern developments are, according to our background and interests: (i) Thomas-Fermi theory and related theories, and (ii) global systems of semilinear elliptic partial-differential equations and the existence of weak solutions and their regularity. Although the direct method in the calculus of variations can naturally be considered part of nonlinear functional analysis, we have not tried to present our material in this way. Some recent books on nonlinear functional analysis in this spirit are those by K. Deimling (Nonlinear Functional Analysis, Springer, Berlin Heidelberg 1985) and E. Zeidler (Nonlinear Functional Analysis and Its Applications, Vols. 1-4; Springer, New York 1986-1990).

## Calculus of Variations

*Topics from the Mathematical Heritage of E. De Giorgi*

**Author**: Diego Pallara**Publisher:**N.A**ISBN:**9788879994149**Category:**Mathematics**Page:**266**View:**3760

## Differential and Integral Equations

**Author**: N.A**Publisher:**N.A**ISBN:**N.A**Category:**Differential equations**Page:**N.A**View:**8342

## Direkte Methoden der Variationsrechnung

*Ein Lehrbuch*

**Author**: Ph. Blanchard,E. Brüning**Publisher:**Springer-Verlag**ISBN:**3709122600**Category:**Science**Page:**280**View:**2827

## Issues in Applied Mathematics: 2011 Edition

**Author**: N.A**Publisher:**ScholarlyEditions**ISBN:**1464965072**Category:**Mathematics**Page:**862**View:**4634

Issues in Applied Mathematics / 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Applied Mathematics. The editors have built Issues in Applied Mathematics: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Applied Mathematics in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Applied Mathematics: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

## Calculus of Variations

*An Introduction to the One-Dimensional Theory with Examples and Exercises*

**Author**: Hansjörg Kielhöfer**Publisher:**Springer**ISBN:**3319711237**Category:**Mathematics**Page:**227**View:**1652

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.

## BIT.

*Numerical mathematics*

**Author**: N.A**Publisher:**N.A**ISBN:**N.A**Category:**Electronic journals**Page:**N.A**View:**8767