Cartesian Currents In The Calculus Of Variations I

Author : Mariano Giaquinta,Giuseppe Modica,Jiri Soucek
Publisher : Springer Science & Business Media
Page : 744 pages
File Size : 49,6 Mb
Release : 1998-08-19
Category : Mathematics
ISBN : 3540640096

Get Book

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 : 53,7 Mb
Release : 1998-08-19
Category : Mathematics
ISBN : 354064010X

Get Book

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 : 55,5 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662062180

Get Book

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 : 51,7 Mb
Release : 2024-06-27
Category : Calculus of variations
ISBN : OCLC:603428349

Get Book

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 : 40,7 Mb
Release : 1998
Category : Electronic
ISBN : OCLC:800844928

Get Book

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 : 51,8 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662062194

Get Book

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 : 54,5 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400881628

Get Book

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 : 55,7 Mb
Release : 1983-11-21
Category : Mathematics
ISBN : 0691083312

Get Book

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 : 55,6 Mb
Release : 2019-06-13
Category : Mathematics
ISBN : 9781000611083

Get Book

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 : Bernard Dacorogna
Publisher : Springer Science & Business Media
Page : 616 pages
File Size : 49,6 Mb
Release : 2007-11-21
Category : Mathematics
ISBN : 9780387552491

Get Book

Direct Methods in the Calculus of Variations by Bernard Dacorogna Pdf

This book is developed for the study of vectorial problems in the calculus of variations. The subject is a very active one and almost half of the book consists of new material. This is a new edition of the earlier book published in 1989 and it is suitable for graduate students. The book has been updated with some new material and examples added. Applications are included.

Author : Stanley Alama,Lia Bronsard,Peter J. Sternberg
Publisher : American Mathematical Soc.
Page : 284 pages
File Size : 44,6 Mb
Release : 2024-06-27
Category : Mathematics
ISBN : 0821873318

Get Book

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 : Ulrich Derigs
Publisher : EOLSS Publications
Page : 438 pages
File Size : 49,8 Mb
Release : 2009-02-09
Category : Electronic
ISBN : 9781905839506

Get Book

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 : Irene Fonseca,Giovanni Leoni
Publisher : Springer Science & Business Media
Page : 602 pages
File Size : 55,7 Mb
Release : 2007-08-22
Category : Science
ISBN : 9780387690063

Get Book

Modern Methods in the Calculus of Variations by Irene Fonseca,Giovanni Leoni Pdf

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.

Author : Haim Brezis,Petru Mironescu
Publisher : Springer Nature
Page : 552 pages
File Size : 54,6 Mb
Release : 2022-01-01
Category : Mathematics
ISBN : 9781071615126

Get Book

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 : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 53,8 Mb
Release : 2024-06-27
Category : Electronic
ISBN : 9789814466363

Get Book

Stability Criteria for Fluid Flows by Anonim Pdf