Cartesian Currents In The Calculus Of Variations

Author : Mariano Giaquinta,Giuseppe Modica,Jiri Soucek
Publisher : Springer Science & Business Media
Page : 744 pages
File Size : 43,8 Mb
Release : 1998-08-19
Category : Mathematics
ISBN : 3540640096

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Cartesian Currents in the Calculus of Variations I by Mariano Giaquinta,Giuseppe Modica,Jiri Soucek Pdf

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

Author : Mariano Giaquinta,Guiseppe Modica,Jiri Soucek
Publisher : Springer Science & Business Media
Page : 728 pages
File Size : 53,9 Mb
Release : 1998-08-19
Category : Mathematics
ISBN : 354064010X

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Cartesian Currents in the Calculus of Variations II by Mariano Giaquinta,Guiseppe Modica,Jiri Soucek Pdf

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

Author : Mariano Giaquinta,Guiseppe Modica,Jiri Soucek
Publisher : Springer Science & Business Media
Page : 717 pages
File Size : 41,7 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662062180

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Cartesian Currents in the Calculus of Variations II by Mariano Giaquinta,Guiseppe Modica,Jiri Soucek Pdf

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.

Author : Mariano Giaquinta,Giuseppe Modica,Jiří Souček
Publisher : Unknown
Page : 128 pages
File Size : 48,9 Mb
Release : 2024-06-30
Category : Calculus of variations
ISBN : OCLC:603428349

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Cartesian currents in the calculus of variations by Mariano Giaquinta,Giuseppe Modica,Jiří Souček Pdf

Author : Mariano Giaquinta
Publisher : Unknown
Page : 697 pages
File Size : 48,8 Mb
Release : 1998
Category : Electronic
ISBN : OCLC:800844928

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Cartesian Currents in the Calculus of Variations II by Mariano Giaquinta Pdf

Author : Mariano Giaquinta,Guiseppe Modica,Jiri Soucek
Publisher : Unknown
Page : 728 pages
File Size : 44,7 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662062194

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Cartesian Currents in the Calculus of Variations II by Mariano Giaquinta,Guiseppe Modica,Jiri Soucek Pdf

Author : Mariano Giaquinta
Publisher : Princeton University Press
Page : 296 pages
File Size : 47,5 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400881628

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Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105), Volume 105 by Mariano Giaquinta Pdf

The description for this book, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105), Volume 105, will be forthcoming.

Author : Mariano Giaquinta
Publisher : Princeton University Press
Page : 312 pages
File Size : 48,8 Mb
Release : 1983-11-21
Category : Mathematics
ISBN : 0691083312

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Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems by Mariano Giaquinta Pdf

The description for this book, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105), Volume 105, will be forthcoming.

Author : Luciano Carbone
Publisher : CRC Press
Page : 211 pages
File Size : 51,7 Mb
Release : 2019-06-13
Category : Mathematics
ISBN : 9781000611083

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Unbounded Functionals in the Calculus of Variations by Luciano Carbone Pdf

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

Author : Luigi Ambrosio,E. Mascolo
Publisher : Springer Science & Business Media
Page : 213 pages
File Size : 54,6 Mb
Release : 2008-01-02
Category : Mathematics
ISBN : 9783540759133

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Calculus of Variations and Nonlinear Partial Differential Equations by Luigi Ambrosio,E. Mascolo Pdf

With a historical overview by Elvira Mascolo

Author : Stanley Alama,Lia Bronsard,Peter J. Sternberg
Publisher : American Mathematical Soc.
Page : 284 pages
File Size : 42,8 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 0821873318

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Singularities in PDE and the Calculus of Variations by Stanley Alama,Lia Bronsard,Peter J. Sternberg Pdf

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.

Author : Frederick J. Almgren
Publisher : American Mathematical Soc.
Page : 638 pages
File Size : 46,6 Mb
Release : 1999
Category : Mathematics
ISBN : 0821810677

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Selected Works of Frederick J. Almgren, Jr. by Frederick J. Almgren Pdf

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

Author : Ulrich Derigs
Publisher : EOLSS Publications
Page : 438 pages
File Size : 48,6 Mb
Release : 2009-02-09
Category : Electronic
ISBN : 9781905839506

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OPTIMIZATION AND OPERATIONS RESEARCH – Volume III by Ulrich Derigs Pdf

Optimization and Operations Research is a component of Encyclopedia of Mathematical Sciences in the global Encyclopedia of Life Support Systems (EOLSS), which is an integrated compendium of twenty one Encyclopedias. The Theme on Optimization and Operations Research is organized into six different topics which represent the main scientific areas of the theme: 1. Fundamentals of Operations Research; 2. Advanced Deterministic Operations Research; 3. Optimization in Infinite Dimensions; 4. Game Theory; 5. Stochastic Operations Research; 6. Decision Analysis, which are then expanded into multiple subtopics, each as a chapter. These four volumes are aimed at the following five major target audiences: University and College students Educators, Professional Practitioners, Research Personnel and Policy Analysts, Managers, and Decision Makers and NGOs.

Author : Haim Brezis,Petru Mironescu
Publisher : Springer Nature
Page : 552 pages
File Size : 44,5 Mb
Release : 2022-01-01
Category : Mathematics
ISBN : 9781071615126

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Sobolev Maps to the Circle by Haim Brezis,Petru Mironescu Pdf

The theory of real-valued Sobolev functions is a classical part of analysis and has a wide range of applications in pure and applied mathematics. By contrast, the study of manifold-valued Sobolev maps is relatively new. The incentive to explore these spaces arose in the last forty years from geometry and physics. This monograph is the first to provide a unified, comprehensive treatment of Sobolev maps to the circle, presenting numerous results obtained by the authors and others. Many surprising connections to other areas of mathematics are explored, including the Monge-Kantorovich theory in optimal transport, items in geometric measure theory, Fourier series, and non-local functionals occurring, for example, as denoising filters in image processing. Numerous digressions provide a glimpse of the theory of sphere-valued Sobolev maps. Each chapter focuses on a single topic and starts with a detailed overview, followed by the most significant results, and rather complete proofs. The “Complements and Open Problems” sections provide short introductions to various subsequent developments or related topics, and suggest newdirections of research. Historical perspectives and a comprehensive list of references close out each chapter. Topics covered include lifting, point and line singularities, minimal connections and minimal surfaces, uniqueness spaces, factorization, density, Dirichlet problems, trace theory, and gap phenomena. Sobolev Maps to the Circle will appeal to mathematicians working in various areas, such as nonlinear analysis, PDEs, geometric analysis, minimal surfaces, optimal transport, and topology. It will also be of interest to physicists working on liquid crystals and the Ginzburg-Landau theory of superconductors.

Author : Robert Weinstock
Publisher : Courier Corporation
Page : 354 pages
File Size : 55,7 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9780486141060

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Calculus of Variations by Robert Weinstock Pdf

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.