Exterior Differential Systems and the Calculus of Variations, P.A. Griffiths

Автор: Robert L. Bryant; S.S. Chern; Robert B. Gardner; H
Название: Exterior Differential Systems
ISBN: 1461397162 ISBN-13(EAN): 9781461397168
Издательство: Springer
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Описание: An exterior differential system is a system of equations on a manifold defined by equating to zero a number of exterior differential forms. A system of partial differential equations, with any number of inde pendent and dependent variables and involving partial derivatives of any order, can be written as an exterior differential system.

Автор: Alexander Plakhov
Название: Exterior Billiards
ISBN: 1489999132 ISBN-13(EAN): 9781489999139
Издательство: Springer
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Описание: Surveying the nature of dynamical systems, in which a point particle alternates between free motion and specular reflections from the boundary of a domain, this book assesses the ways in which they can be applied to aerodynamics as well as geometrical optics.

Автор: Mariano Giaquinta; Stefan Hildebrandt
Название: Calculus of Variations I
ISBN: 364208074X ISBN-13(EAN): 9783642080746
Издательство: Springer
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Описание: This book describes the classical aspects of the variational calculus which are of interest to analysts, geometers and physicists alike. Volume 1 deals with the for- mal apparatus of the variational calculus and with nonparametric field theory, whereas Volume 2 treats parametric variational problems as well as Hamilton- Jacobi theory and the classical theory of partial differential equations of first ordel;. In a subsequent treatise we shall describe developments arising from Hilbert's 19th and 20th problems, especially direct methods and regularity theory. Of the classical variational calculus we have particularly emphasized the often neglected theory of inner variations, i. e. of variations of the independent variables, which is a source of useful information such as mono tonicity for- mulas, conformality relations and conservation laws. The combined variation of dependent and independent variables leads to the general conservation laws of Emmy Noether, an important tool in exploiting symmetries. Other parts of this volume deal with Legendre-Jacobi theory and with field theories. In particular we give a detailed presentation of one-dimensional field theory for nonpara- metric and parametric integrals and its relations to Hamilton-Jacobi theory, geometrical optics and point mechanics. Moreover we discuss various ways of exploiting the notion of convexity in the calculus of variations, and field theory is certainly the most subtle method to make use of convexity. We also stress the usefulness of the concept of a null Lagrangian which plays an important role in we give an exposition of Hamilton-Jacobi several instances.

Автор: S. Hildebrandt; F. Bethuel; M. Struwe; G. Huisken;
Название: Calculus of Variations and Geometric Evolution Problems
ISBN: 3540659773 ISBN-13(EAN): 9783540659778
Издательство: Springer
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Описание: The international summer school on Calculus of Variations and Geometric Evolution Problems was held at Cetraro, Italy, 1996. The contributions to this volume reflect quite closely the lectures given at Cetraro.

Автор: Dmitry V. Zenkov
Название: The Inverse Problem of the Calculus of Variations
ISBN: 9462391084 ISBN-13(EAN): 9789462391086
Издательство: Springer
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Описание: The Inverse Problem of the Calculus of Variations

Автор: Mariano Giaquinta; Giuseppe Modica; Jiri Soucek
Название: Cartesian Currents in the Calculus of Variations I
ISBN: 3642083749 ISBN-13(EAN): 9783642083747
Издательство: Springer
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Автор: Mariano Giaquinta; Guiseppe Modica; Jiri Soucek
Название: Cartesian Currents in the Calculus of Variations II
ISBN: 3642083757 ISBN-13(EAN): 9783642083754
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Описание: 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.

Автор: Struwe Michael
Название: Plateau`s Problem and the Calculus of Variations. (MN-35):
ISBN: 0691607753 ISBN-13(EAN): 9780691607757
Издательство: Wiley
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Описание: This book is meant to give an account of recent developments in the theory of Plateau`s problem for parametric minimal surfaces and surfaces of prescribed constant mean curvature ("H-surfaces") and its analytical framework. A comprehensive overview of the classical existence and regularity theory for disc-type minimal and H-surfaces is given and re

Автор: Mariano Giaquinta; Stefan Hildebrandt
Название: Calculus of Variations II
ISBN: 3642081924 ISBN-13(EAN): 9783642081927
Издательство: Springer
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Цена: 18161.00 р.
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Описание: This book describes the classical aspects of the variational calculus which are of interest to analysts, geometers and physicists alike. Volume 1 deals with the for- mal apparatus of the variational calculus and with nonparametric field theory, whereas Volume 2 treats parametric variational problems as weIl as Hamilton- Jacobi theory and the classical theory of partial differential equations of first order. In a subsequent treatise we shall describe developments arising from Hilbert's 19th and 20th problems, especially direct methods and regularity theory. Of the classical variational calculus we have particularly emphasized the often neglected theory of inner variations, i. e. of variations of the independent variables, which is a source of useful information such as monotonicity for- mulas, conformality relations and conservation laws. The combined variation of dependent and independent variables leads to the general conservation laws of Emmy Noether, an important tool in exploiting symmetries. Other parts of this volume deal with Legendre-Jacobi theory and with field theories. In particular we give a detailed presentation of one-dimensional field theory for non para- metric and parametric integrals and its relations to Hamilton-Jacobi theory, geometrieal optics and point mechanics. Moreover we discuss various ways of exploiting the notion of convexity in the calculus of variations, and field theory is certainly the most subtle method to make use of convexity. We also stress the usefulness of the concept of a null Lagrangian which plays an important role in several instances.