Cartesian Currents In The Calculus Of Variations Ii

Author : Mariano Giaquinta,Giuseppe Modica,Jiri Soucek
Publisher : Springer Science & Business Media
Page : 744 pages
File Size : 42,9 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 : 48,5 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 : 55,6 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
Publisher : Unknown
Page : 697 pages
File Size : 48,5 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 : 45,7 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,Giuseppe Modica,Jiří Souček
Publisher : Unknown
Page : 128 pages
File Size : 43,7 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 : Luciano Carbone
Publisher : CRC Press
Page : 211 pages
File Size : 43,6 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 : Mariano Giaquinta
Publisher : Princeton University Press
Page : 296 pages
File Size : 48,7 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 : Stanley Alama,Lia Bronsard,Peter J. Sternberg
Publisher : American Mathematical Soc.
Page : 284 pages
File Size : 50,5 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 : Mariano Giaquinta
Publisher : Princeton University Press
Page : 312 pages
File Size : 54,8 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 : Haim Brezis,Petru Mironescu
Publisher : Springer Nature
Page : 552 pages
File Size : 40,5 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 : Filip Rindler
Publisher : Springer
Page : 444 pages
File Size : 40,5 Mb
Release : 2018-06-20
Category : Mathematics
ISBN : 9783319776378

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Calculus of Variations by Filip Rindler Pdf

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.

Author : Ulrich Derigs
Publisher : EOLSS Publications
Page : 438 pages
File Size : 42,9 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 : Demeter Krupka,David Saunders
Publisher : Elsevier
Page : 1243 pages
File Size : 49,9 Mb
Release : 2011-08-11
Category : Mathematics
ISBN : 9780080556734

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Handbook of Global Analysis by Demeter Krupka,David Saunders Pdf

This is a comprehensive exposition of topics covered by the American Mathematical Society’s classification “Global Analysis , dealing with modern developments in calculus expressed using abstract terminology. It will be invaluable for graduate students and researchers embarking on advanced studies in mathematics and mathematical physics.This book provides a comprehensive coverage of modern global analysis and geometrical mathematical physics, dealing with topics such as; structures on manifolds, pseudogroups, Lie groupoids, and global Finsler geometry; the topology of manifolds and differentiable mappings; differential equations (including ODEs, differential systems and distributions, and spectral theory); variational theory on manifolds, with applications to physics; function spaces on manifolds; jets, natural bundles and generalizations; and non-commutative geometry. - Comprehensive coverage of modern global analysis and geometrical mathematical physics- Written by world-experts in the field- Up-to-date contents

Author : Fanghua Lin
Publisher : World Scientific
Page : 280 pages
File Size : 42,9 Mb
Release : 2008
Category : Mathematics
ISBN : 9789812779533

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The Analysis of Harmonic Maps and Their Heat Flows by Fanghua Lin Pdf

This book contains the proceedings of the Fourth Meeting on CPT and Lorentz Symmetry, held at Indiana University in Bloomington on August 8-11, 2007. The Meeting focused on experimental tests of these fundamental symmetries and on important theoretical issues, including scenarios for possible relativity violations. Experimental subjects covered include: astrophysical observations, clock-comparison measurements, cosmological birefringence, electromagnetic resonant cavities, gravitational tests, matter interferometry, muon behavior, neutrino oscillations, oscillations and decays of neutral mesons, particle-antiparticle comparisons, post-Newtonian gravity, space-based missions, spectroscopy of hydrogen and antihydrogen, and spin-polarized matter.Theoretical topics covered include: physical effects at the level of the Standard Model, General Relativity, and beyond; the possible origins and mechanisms for Lorentz and CPT violations; and associated issues in field theory, particle physics, gravity, and string theory. The contributors consist of the leading experts in this very active research field.