Partial Regularity For Harmonic Maps And Related Problems
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Partial Regularity For Harmonic Maps And Related Problems
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Author : Roger Moser
language : en
Publisher: World Scientific
Release Date : 2005
Partial Regularity For Harmonic Maps And Related Problems written by Roger Moser and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
The book presents a collection of results pertaining to the partial regularity of solutions to various variational problems, all of which are connected to the Dirichlet energy of maps between Riemannian manifolds, and thus related to the harmonic map problem. The topics covered include harmonic maps and generalized harmonic maps; certain perturbed versions of the harmonic map equation; the harmonic map heat flow; and the Landau-Lifshitz (or Landau-Lifshitz-Gilbert) equation. Since the methods in regularity theory of harmonic maps are quite subtle, it is not immediately clear how they can be applied to certain problems that arise in applications. The book discusses in particular this question.
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.
Partial Regularity For Harmonic Maps And Related Problems
DOWNLOAD
Author : Roger Moser
language : en
Publisher: World Scientific
Release Date : 2005
Partial Regularity For Harmonic Maps And Related Problems written by Roger Moser and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
The book presents a collection of results pertaining to the partial regularity of solutions to various variational problems, all of which are connected to the Dirichlet energy of maps between Riemannian manifolds, and thus related to the harmonic map problem. The topics covered include harmonic maps and generalized harmonic maps; certain perturbed versions of the harmonic map equation; the harmonic map heat flow; and the Landau-Lifshitz (or Landau-Lifshitz-Gilbert) equation. Since the methods in regularity theory of harmonic maps are quite subtle, it is not immediately clear how they can be applied to certain problems that arise in applications. The book discusses in particular this question.
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.
C1 Ss Partial C 1 Beta Partial Regularity Of P Harmonic Maps At The Free Boundary
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Author : Thomas Müller
language : en
Publisher:
Release Date : 1999
C1 Ss Partial C 1 Beta Partial Regularity Of P Harmonic Maps At The Free Boundary written by Thomas Müller and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.
Topics In The Calculus Of Variations
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Author : Martin Fuchs
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Topics In The Calculus Of Variations written by Martin Fuchs 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 Technology & Engineering categories.
This book illustrates two basic principles in the calculus of variations which are the question of existence of solutions and closely related the problem of regularity of minimizers. Chapter one studies variational problems for nonquadratic energy functionals defined on suitable classes of vectorvalued functions where also nonlinear constraints are incorporated. Problems of this type arise for mappings between Riemannian manifolds or in nonlinear elasticity. Using direct methods the existence of generalized minimizers is rather easy to establish and it is then shown that regularity holds up to a set of small measure. Chapter two contains a short introduction into Geometric Measure Theory which serves as a basis for developing an existence theory for (generalized) manifolds with prescribed mean curvature form and boundary in arbitrary dimensions and codimensions. One major aspect of the book is to concentrate on techniques and to present methods which turn out to be useful for applications in regularity theorems as well as for existence problems.
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.
Nonlinear Partial Differential Equations And Related Topics
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Author : Arina A. Arkhipova
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Nonlinear Partial Differential Equations And Related Topics written by Arina A. Arkhipova and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
"St. Petersburg PDE seminar, special session dedicated to N.N. Uraltseva's [75th] anniversary, June 2009"--P. [vi].
Nonlinear Dispersive Waves And Fluids
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Author : Avy Soffer
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-03-12
Nonlinear Dispersive Waves And Fluids written by Avy Soffer and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-12 with Nonlinear wave equations categories.
This volume contains the proceedings of the AMS Special Session on Spectral Calculus and Quasilinear Partial Differential Equations and the AMS Special Session on PDE Analysis on Fluid Flows, which were held in January 2017 in Atlanta, Georgia. These two sessions shared the underlying theme of the analysis aspect of evolutionary PDEs and mathematical physics. The articles address the latest trends and perspectives in the area of nonlinear dispersive equations and fluid flows. The topics mainly focus on using state-of-the-art methods and techniques to investigate problems of depth and richness arising in quantum mechanics, general relativity, and fluid dynamics.
Some Contributions To Geometric Variational Problems Involving Nonlocal Energies
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Author : Marc Pegon
language : en
Publisher:
Release Date : 2019
Some Contributions To Geometric Variational Problems Involving Nonlocal Energies written by Marc Pegon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
This thesis is dedicated to the study of two separate geometric variational problems involving nonlocal energies: firstly, the geometry and singularities of fractional harmonic maps,and secondly, an iso perimetric problem with a repulsive integrable potential inspired by Gamow's liquid drop model for the atomic nucleus. On the first topic, we improve already-known results for minimizing 1/2-harmonic maps when the target manifold is a sphere by reducing the upperbound on the Haudorff dimension of the singular set, i.e., the set of points of discontinuity. Wealso characterize so-called minimizing 1/2-harmonic tangent maps from the plane into the unit circle S1, shedding light on the behavior of minimizing 1/2-harmonic maps from R2into S1 near singularities. Finally, when s ∈ (0, 1), we prove partial regularity results for s-harmonic maps into spheres in the stationary and minimizing case, obtaining sharp estimates on the Hausdorffd imension of the set of singularities, depending on the value of s. As for the second topic of the thesis, we study a minimization problem on sets of finite perimeter under a volume constraint, where the functional is the sum of a cohesive perimeter term and a repulsive term given by a general integrable symmetric kernel on Rn. We show that under reasonable assumptions on the behavior near the origin and on some of the moments of this kernel - which include physically relevant Bessel potentials - the problem admits large mass (or volume) minimizers. In addition,after normalization, those minimizers converge to the unit ball as the mass goes to infinity. By studying the stability of the ball, we show that without these assumptions, symmetry breaking can occur, that is, there are cases when the problem admits minimizers which cannot be the ball.
