Calculus Of Variations And Harmonic Maps
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Translations Of Mathematical Monographs
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Author :
language : en
Publisher:
Release Date : 1962
Translations Of Mathematical Monographs written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1962 with Calculus of variations categories.
Theorems On Regularity And Singularity Of Energy Minimizing Maps
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Author : Leon Simon
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Theorems On Regularity And Singularity Of Energy Minimizing Maps written by Leon Simon and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The aim of these lecture notes is to give an essentially self-contained introduction to the basic regularity theory for energy minimizing maps, including recent developments concerning the structure of the singular set and asymptotics on approach to the singular set. Specialized knowledge in partial differential equations or the geometric calculus of variations is not required; a good general background in mathematical analysis would be adequate preparation.
Harmonic Mappings Twistors And Sigma Models
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Author : Paul Gauduchon
language : en
Publisher: World Scientific
Release Date : 1988-10-01
Harmonic Mappings Twistors And Sigma Models written by Paul Gauduchon and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-10-01 with Mathematics categories.
Harmonic mappings have played in recent years and will likely to play in the future an important role in Differential Geometry and Theoretical Physics, where they are known as s-models. These Proceedings develop both aspects of the theory, with a special attention to the constructive methods, in particular the so-called twistorial approach. It includes expository articles on the twistorial methods, the various appearence of σ-models in Physics, the powerful analytic theory of regularity of SCHOEN-UHLENBECK.
An Introduction To The Regularity Theory For Elliptic Systems Harmonic Maps And Minimal Graphs
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Author : Mariano Giaquinta
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-30
An Introduction To The Regularity Theory For Elliptic Systems Harmonic Maps And Minimal Graphs written by Mariano Giaquinta and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-30 with Mathematics categories.
This volume deals with the regularity theory for elliptic systems. We may find the origin of such a theory in two of the problems posed by David Hilbert in his celebrated lecture delivered during the International Congress of Mathematicians in 1900 in Paris: 19th problem: Are the solutions to regular problems in the Calculus of Variations always necessarily analytic? 20th problem: does any variational problem have a solution, provided that certain assumptions regarding the given boundary conditions are satisfied, and provided that the notion of a solution is suitably extended? During the last century these two problems have generated a great deal of work, usually referred to as regularity theory, which makes this topic quite relevant in many fields and still very active for research. However, the purpose of this volume, addressed mainly to students, is much more limited. We aim to illustrate only some of the basic ideas and techniques introduced in this context, confining ourselves to important but simple situations and refraining from completeness. In fact some relevant topics are omitted. Topics include: harmonic functions, direct methods, Hilbert space methods and Sobolev spaces, energy estimates, Schauder and L^p-theory both with and without potential theory, including the Calderon-Zygmund theorem, Harnack's and De Giorgi-Moser-Nash theorems in the scalar case and partial regularity theorems in the vector valued case; energy minimizing harmonic maps and minimal graphs in codimension 1 and greater than 1. In this second deeply revised edition we also included the regularity of 2-dimensional weakly harmonic maps, the partial regularity of stationary harmonic maps, and their connections with the case p=1 of the L^p theory, including the celebrated results of Wente and of Coifman-Lions-Meyer-Semmes.
Geometry Of Harmonic Maps
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Author : Yuanlong Xin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometry Of Harmonic Maps written by Yuanlong Xin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Harmonic maps are solutions to a natural geometrical variational prob lem. This notion grew out of essential notions in differential geometry, such as geodesics, minimal surfaces and harmonic functions. Harmonic maps are also closely related to holomorphic maps in several complex variables, to the theory of stochastic processes, to nonlinear field theory in theoretical physics, and to the theory of liquid crystals in materials science. During the past thirty years this subject has been developed extensively. The monograph is by no means intended to give a complete description of the theory of harmonic maps. For example, the book excludes a large part of the theory of harmonic maps from 2-dimensional domains, where the methods are quite different from those discussed here. The first chapter consists of introductory material. Several equivalent definitions of harmonic maps are described, and interesting examples are presented. Various important properties and formulas are derived. Among them are Bochner-type formula for the energy density and the second varia tional formula. This chapter serves not only as a basis for the later chapters, but also as a brief introduction to the theory. Chapter 2 is devoted to the conservation law of harmonic maps. Em phasis is placed on applications of conservation law to the mono tonicity formula and Liouville-type theorems.
Seminar On Nonlinear Partial Differential Equations
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Author : S.S. Chern
language : en
Publisher: Springer
Release Date : 1984-11-01
Seminar On Nonlinear Partial Differential Equations written by S.S. Chern and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-11-01 with Mathematics categories.
When the Mathematical Sciences Research Institute was started in the Fall of 1982, one of the programs was "non-linear partial differential equations". A seminar was organized whose audience consisted of graduate students of the University and mature mathematicians who are not experts in the field. This volume contains 18 of these lectures. An effort is made to have an adequate Bibliography for further information. The Editor wishes to take this opportunity to thank all the speakers and the authors of the articles presented in this volume for their cooperation. S. S. Chern, Editor Table of Contents Geometrical and Analytical Questions Stuart S. Antman 1 in Nonlinear Elasticity An Introduction to Euler's Equations Alexandre J. Chorin 31 for an Incompressible Fluid Linearizing Flows and a Cohomology Phillip Griffiths 37 Interpretation of Lax Equations The Ricci Curvature Equation Richard Hamilton 47 A Walk Through Partial Differential Fritz John 73 Equations Remarks on Zero Viscosity Limit for Tosio Kato 85 Nonstationary Navier-Stokes Flows with Boundary Free Boundary Problems in Mechanics Joseph B. Keller 99 The Method of Partial Regularity as Robert V.
Harmonic Maps
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Author : James Eells
language : en
Publisher: World Scientific
Release Date : 1992
Harmonic Maps written by James Eells and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
These original research papers, written during a period of over a quarter of a century, have two main objectives. The first is to lay the foundations of the theory of harmonic maps between Riemannian Manifolds, and the second to establish various existence and regularity theorems as well as the explicit constructions of such maps.
Harmonic Maps Conservation Laws And Moving Frames
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Author : Frédéric Hélein
language : en
Publisher: Cambridge University Press
Release Date : 2002-06-13
Harmonic Maps Conservation Laws And Moving Frames written by Frédéric Hélein and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-06-13 with Mathematics categories.
Publisher Description
Handbook Of Global Analysis
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Author : Demeter Krupka
language : en
Publisher: Elsevier
Release Date : 2011-08-11
Handbook Of Global Analysis written by Demeter Krupka and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-11 with Mathematics categories.
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
The Analysis Of Harmonic Maps And Their Heat Flows
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Author : Fanghua Lin
language : en
Publisher: World Scientific
Release Date : 2008
The Analysis Of Harmonic Maps And Their Heat Flows written by Fanghua Lin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Science categories.
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.