Two Dimensional Geometric Variational Problems
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Two Dimensional Geometric Variational Problems
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Author : Jürgen Jost
language : en
Publisher:
Release Date : 1991-03-29
Two Dimensional Geometric Variational Problems written by Jürgen Jost and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-03-29 with Mathematics categories.
This monograph treats variational problems for mappings from a surface equipped with a conformal structure into Euclidean space or a Riemannian manifold. Presents a general theory of such variational problems, proving existence and regularity theorems with particular conceptual emphasis on the geometric aspects of the theory and thorough investigation of the connections with complex analysis. Among the topics covered are: Plateau's problem, the regularity theory of solutions, a variational approach for obtaining various conformal representation theorems, a general existence theorem for harmonic mappings, and a new approach to Teichmuller theory via harmonic maps.
Unstable Solutions Of Two Dimensional Geometric Variational Problems
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Author : Jürgen Jost
language : de
Publisher:
Release Date : 1991
Unstable Solutions Of Two Dimensional Geometric Variational Problems written by Jürgen Jost and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with categories.
Twodimensional Geometric Variational Problems
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Author : Jürgen Jost
language : en
Publisher:
Release Date : 1987
Twodimensional Geometric Variational Problems written by Jürgen Jost and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with categories.
Variational Problems In Topology
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Author : A.T. Fomenko
language : en
Publisher: Routledge
Release Date : 2019-06-21
Variational Problems In Topology written by A.T. Fomenko and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-21 with Mathematics categories.
Many of the modern variational problems of topology arise in different but overlapping fields of scientific study: mechanics, physics and mathematics. In this work, Professor Fomenko offers a concise and clear explanation of some of these problems (both solved and unsolved), using current methods of analytical topology. His book falls into three interrelated sections. The first gives an elementary introduction to some of the most important concepts of topology used in modern physics and mechanics: homology and cohomology, and fibration. The second investigates the significant role of Morse theory in modern aspects of the topology of smooth manifolds, particularly those of three and four dimensions. The third discusses minimal surfaces and harmonic mappings, and presents a number of classic physical experiments that lie at the foundations of modern understanding of multidimensional variational calculus. The author's skilful exposition of these topics and his own graphic illustrations give an unusual motivation to the theory expounded, and his work is recommended reading for specialists and non-specialists alike, involved in the fields of physics and mathematics at both undergraduate and graduate levels.
One Dimensional Variational Problems
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Author : Giuseppe Buttazzo
language : en
Publisher: Oxford University Press
Release Date : 1998
One Dimensional Variational Problems written by Giuseppe Buttazzo and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
While easier to solve and accessible to a broader range of students, one-dimensional variational problems and their associated differential equations exhibit many of the same complex behavior of higher-dimensional problems. This book, the first moden introduction, emphasizes direct methods and provides an exceptionally clear view of the underlying theory.
Selected Chapters In The Calculus Of Variations
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Author : Jürgen Moser
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Selected Chapters In The Calculus Of Variations written by Jürgen Moser 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.
0.1 Introduction These lecture notes describe a new development in the calculus of variations which is called Aubry-Mather-Theory. The starting point for the theoretical physicist Aubry was a model for the descrip tion of the motion of electrons in a two-dimensional crystal. Aubry investigated a related discrete variational problem and the corresponding minimal solutions. On the other hand, Mather started with a specific class of area-preserving annulus mappings, the so-called monotone twist maps. These maps appear in mechanics as Poincare maps. Such maps were studied by Birkhoff during the 1920s in several papers. In 1982, Mather succeeded to make essential progress in this field and to prove the existence of a class of closed invariant subsets which are now called Mather sets. His existence theorem is based again on a variational principle. Although these two investigations have different motivations, they are closely re lated and have the same mathematical foundation. We will not follow those ap proaches but will make a connection to classical results of Jacobi, Legendre, Weier strass and others from the 19th century. Therefore in Chapter I, we will put together the results of the classical theory which are the most important for us. The notion of extremal fields will be most relevant. In Chapter II we will investigate variational problems on the 2-dimensional torus. We will look at the corresponding global minimals as well as at the relation be tween minimals and extremal fields. In this way, we will be led to Mather sets.
Existence And Regularity Almost Everywhere Of Solutions To Elliptic Variational Problems With Constraints
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Author : Frederick J. Almgren
language : en
Publisher: American Mathematical Soc.
Release Date : 1976
Existence And Regularity Almost Everywhere Of Solutions To Elliptic Variational Problems With Constraints written by Frederick J. Almgren 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 1976 with Calculus of variations categories.
Geometric Variational Problems Related To Symplectic Geometry
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Author : William P. Minicozzi (II.)
language : en
Publisher:
Release Date : 1994
Geometric Variational Problems Related To Symplectic Geometry written by William P. Minicozzi (II.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with categories.
Branching Solutions To One Dimensional Variational Problems
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Author : Alexandr Ivanov
language : en
Publisher: World Scientific
Release Date : 2001-01-17
Branching Solutions To One Dimensional Variational Problems written by Alexandr Ivanov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-17 with Mathematics categories.
This book deals with the new class of one-dimensional variational problems — the problems with branching solutions. Instead of extreme curves (mappings of a segment to a manifold) we investigate extreme networks, which are mappings of graphs (one-dimensional cell complexes) to a manifold. Various applications of the approach are presented, such as several generalizations of the famous Steiner problem of finding the shortest network spanning given points of the plane.
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.