Download or read book Cartesian Currents in the Calculus of Variations I written by Mariano Giaquinta and published by Springer Science & Business Media. This book was released on 1998-08-19 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph (in two volumes) deals with non scalar variational problems arising in geometry, as harmonic mappings between Riemannian manifolds and minimal graphs, and in physics, as stable equilibrium configuations in nonlinear elasticity or for liquid crystals. The presentation is selfcontained and accessible to non specialists. Topics are treated as far as possible in an elementary way, illustrating results with simple examples; in principle, chapters and even sections are readable independently of the general context, so that parts can be easily used for graduate courses. Open questions are often mentioned and the final section of each chapter discusses references to the literature and sometimes supplementary results. Finally, a detailed Table of Contents and an extensive Index are of help to consult this monograph
Download or read book Cartesian Currents in the Calculus of Variations II written by Mariano Giaquinta and published by Springer Science & Business Media. This book was released on 1998-08-19 with total page 728 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph (in two volumes) deals with non scalar variational problems arising in geometry, as harmonic mappings between Riemannian manifolds and minimal graphs, and in physics, as stable equilibrium configuations in nonlinear elasticity or for liquid crystals. The presentation is selfcontained and accessible to non specialists. Topics are treated as far as possible in an elementary way, illustrating results with simple examples; in principle, chapters and even sections are readable independently of the general context, so that parts can be easily used for graduate courses. Open questions are often mentioned and the final section of each chapter discusses references to the literature and sometimes supplementary results. Finally, a detailed Table of Contents and an extensive Index are of help to consult this monograph
Download or read book Cartesian Currents in the Calculus of Variations II written by Mariano Giaquinta and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 717 pages. Available in PDF, EPUB and Kindle. Book excerpt: Non-scalar variational problems appear in different fields. In geometry, for in stance, we encounter the basic problems of harmonic maps between Riemannian manifolds and of minimal immersions; related questions appear in physics, for example in the classical theory of a-models. Non linear elasticity is another example in continuum mechanics, while Oseen-Frank theory of liquid crystals and Ginzburg-Landau theory of superconductivity require to treat variational problems in order to model quite complicated phenomena. Typically one is interested in finding energy minimizing representatives in homology or homotopy classes of maps, minimizers with prescribed topological singularities, topological charges, stable deformations i. e. minimizers in classes of diffeomorphisms or extremal fields. In the last two or three decades there has been growing interest, knowledge, and understanding of the general theory for this kind of problems, often referred to as geometric variational problems. Due to the lack of a regularity theory in the non scalar case, in contrast to the scalar one - or in other words to the occurrence of singularities in vector valued minimizers, often related with concentration phenomena for the energy density - and because of the particular relevance of those singularities for the problem being considered the question of singling out a weak formulation, or completely understanding the significance of various weak formulations becames non trivial.
Download or read book Cartesian currents in the calculus of variations written by Mariano Giaquinta and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Cartesian Currents in the Calculus of Variations II written by Mariano Giaquinta and published by . This book was released on 1998 with total page 697 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Cartesian Currents in the Calculus of Variations II written by Mariano Giaquinta and published by . This book was released on 2014-01-15 with total page 728 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Cartesian Currents in the Calculus of Variations I written by Mariano Giaquinta and published by Springer. This book was released on 1998-08-19 with total page 711 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph (in two volumes) deals with non scalar variational problems arising in geometry, as harmonic mappings between Riemannian manifolds and minimal graphs, and in physics, as stable equilibrium configuations in nonlinear elasticity or for liquid crystals. The presentation is selfcontained and accessible to non specialists. Topics are treated as far as possible in an elementary way, illustrating results with simple examples; in principle, chapters and even sections are readable independently of the general context, so that parts can be easily used for graduate courses. Open questions are often mentioned and the final section of each chapter discusses references to the literature and sometimes supplementary results. Finally, a detailed Table of Contents and an extensive Index are of help to consult this monograph
Download or read book Cartesian Currents in the Calculus of Variations V II written by Mariano Giaquinta and published by . This book was released on 1998 with total page 697 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Cartesian Currents in the Calculus of Variations written by Mariano Giaquinta and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Cartesian Currents in the Calculus of Variations Cartesian currents written by Mariano Giaquinta and published by . This book was released on 1998 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems AM 105 Volume 105 written by Mariano Giaquinta and published by Princeton University Press. This book was released on 2016-03-02 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description for this book, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105), Volume 105, will be forthcoming.
Download or read book Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems written by Mariano Giaquinta and published by Princeton University Press. This book was released on 1983-11-21 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description for this book, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105), Volume 105, will be forthcoming.
Download or read book Unbounded Functionals in the Calculus of Variations written by Luciano Carbone and published by CRC Press. This book was released on 2019-06-13 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last few decades, research in elastic-plastic torsion theory, electrostatic screening, and rubber-like nonlinear elastomers has pointed the way to some interesting new classes of minimum problems for energy functionals of the calculus of variations. This advanced-level monograph addresses these issues by developing the framework of a gener
Download or read book Singularities in PDE and the Calculus of Variations written by Stanley Alama and published by American Mathematical Soc.. This book was released on with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains papers presented at the "Workshop on Singularities in PDE and the Calculus of Variations" at the CRM in July 2006. The main theme of the meeting was the formation of geometrical singularities in PDE problems with a variational formulation. These equations typically arise in some applications (to physics, engineering, or biology, for example) and their resolution often requires a combination of methods coming from areas such as functional and harmonic analysis, differential geometry and geometric measure theory. Among the PDE problems discussed were: the Cahn-Hilliard model of phase transitions and domain walls; vortices in Ginzburg-Landau type models for superconductivity and superfluidity; the Ohna-Kawasaki model for di-block copolymers; models of image enhancement; and Monge-Ampere functions. The articles give a sampling of problems and methods in this diverse area of mathematics, which touches a large part of modern mathematics and its applications.
Download or read book Calculus of Variations and Nonlinear Partial Differential Equations written by Luigi Ambrosio and published by Springer Science & Business Media. This book was released on 2008-01-02 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: With a historical overview by Elvira Mascolo
Download or read book Calculus of Variations written by Filip Rindler and published by Springer. This book was released on 2018-06-20 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a comprehensive introduction to the classical and modern calculus of variations, serving as a useful reference to advanced undergraduate and graduate students as well as researchers in the field. Starting from ten motivational examples, the book begins with the most important aspects of the classical theory, including the Direct Method, the Euler-Lagrange equation, Lagrange multipliers, Noether’s Theorem and some regularity theory. Based on the efficient Young measure approach, the author then discusses the vectorial theory of integral functionals, including quasiconvexity, polyconvexity, and relaxation. In the second part, more recent material such as rigidity in differential inclusions, microstructure, convex integration, singularities in measures, functionals defined on functions of bounded variation (BV), and Γ-convergence for phase transitions and homogenization are explored. While predominantly designed as a textbook for lecture courses on the calculus of variations, this book can also serve as the basis for a reading seminar or as a companion for self-study. The reader is assumed to be familiar with basic vector analysis, functional analysis, Sobolev spaces, and measure theory, though most of the preliminaries are also recalled in the appendix.
Download or read book Selected Works of Frederick J Almgren Jr written by Frederick J. Almgren and published by American Mathematical Soc.. This book was released on 1999 with total page 638 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers a unique collection of some of the work of Frederick J. Almgren, Jr., the man most noted for defining the shape of geometric variational problems and for his role in founding The Geometry Center. Included in the volume are the following: a summary by Sheldon Chang of the famous 1700 page paper on singular sets of area-minimizing $m$-dimensional surfaces in $Rn$, a detailed summary by Brian White of Almgren's contributions to mathematics, his own announcements of several longer papers, important shorter papers, and memorable expository papers. Almgren's enthusiasm for the subject and his ability to locate mathematically beautiful problems that were "ready to be solved" attracted many students who further expanded the subject into new areas. Many of these former students are now known for the clarity of their expositions and for the beauty of the problems that they work on. As Almgren's former graduate student, wife, and colleague, Professor Taylor has compiled an important volume on an extraordinary mathematician. This collection presents a fine comprehensive view of the man's mathematical legacy
