Topics in the Calculus of Variations (Advanced Lectures in Mathematics)

Fuchs, Martin:

ISBN 10: 3528066237 ISBN 13: 9783528066239

Edit� par Friedrich Vieweg & Sohn Verlagsgesellschaft mbH, 1998

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Synopsis :

This work illustrates two basic principles in the calculus of variations - the questions 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 vector-valued functions where nonlinear constraints are also incorporated. Problems of this type arise for mappings between Riemannian manifolds or in nonlinear elasticity. Using direct methods for 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 co-dimensions. A major aspect of the book is that it concentrates on techniques, and presents methods which turn out to be useful for applications in regularity theorems, as well as for existence problems.

� propos de l?auteur: Prof. Dr. Martin Fuchs ist an der Universit�t des Saarlandes im Bereich Variationsrechnung und partielle Differentialgleichungen mit Bez�gen zur mathematischen Physik und Differentialgeometrie t�tig.

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Titre : Topics in the Calculus of Variations (...
�diteur : Friedrich Vieweg & Sohn Verlagsgesellschaft mbH
Date d'�dition : 1998
Reliure : paperback
Etat : Befriedigend

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Topics in the Calculus of Variations

Fuchs, Martin

Edit� par De Gruyter Saur, 1994

ISBN 10 : 3528066237 ISBN 13 : 9783528066239

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Topics in the Calculus of Variations

Martin Fuchs

Edit� par Vieweg+Teubner Verlag, 1994

ISBN 10 : 3528066237 ISBN 13 : 9783528066239

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Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Prof. Dr. Martin Fuchs ist an der Universitaet des Saarlandes im Bereich Variationsrechnung und partielle Differentialgleichungen mit Bezuegen zur mathematischen Physik und Differentialgeometrie taetig.This book illustrates two basic principles in the calc. N� de r�f. du vendeur 4866977

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Topics in the Calculus of Variations

Martin Fuchs

Edit� par Vieweg & Teubner, 1994

ISBN 10 : 3528066237 ISBN 13 : 9783528066239

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Topics in the Calculus of Variations

Martin Fuchs

Edit� par Vieweg+Teubner Verlag, Vieweg+Teubner Verlag Jan 1994, 1994

ISBN 10 : 3528066237 ISBN 13 : 9783528066239

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Taschenbuch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This report grew out of a series of lectures given at the East China Institute of Technology, Nanjing, during September 1992. The purpose of this book is to make beginning research students familiar with some problems in varia tional calculus which have been chosen following my personal taste but with the attempt to illustrate two basic principles in the calculus of variations which are the fundamental question of existence of (generalized) solutions and closely related the question of regularity. Chapter one is devoted to the study of variational integrals for vectorvalued functions which began with the pioneering work of Morrey [68] in the thirties. We concentrate on problems where also nonlinear side conditions are imposed on the classes of admissi ble comparison functions. As special cases we include mappings whose range is forced to lie in some Riemannian manifold possibly with boundary or functions whose Jacobian is required to be strictly positive. The variational integrals under consideration are typically nonquadratic with respect to the gradient which immediately leads us to classes of degenerate elliptic systems. Let us mention some of the most important applications: - p-harmonic maps between Riemannian manifolds - systems of degenerate variational inequalities - model problems in nonlinear elasticity. Usually by working in appropriate Sobolev spaces, the existence of gener alized solutions is rather easy to establish (see [7]) but leads to apriori dis continuous functions. 160 pp. Englisch. N� de r�f. du vendeur 9783528066239

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Topics in the Calculus of Variations

Martin Fuchs

Edit� par Vieweg+Teubner Verlag, 1994

ISBN 10 : 3528066237 ISBN 13 : 9783528066239

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Taschenbuch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - This report grew out of a series of lectures given at the East China Institute of Technology, Nanjing, during September 1992. The purpose of this book is to make beginning research students familiar with some problems in varia tional calculus which have been chosen following my personal taste but with the attempt to illustrate two basic principles in the calculus of variations which are the fundamental question of existence of (generalized) solutions and closely related the question of regularity. Chapter one is devoted to the study of variational integrals for vectorvalued functions which began with the pioneering work of Morrey [68] in the thirties. We concentrate on problems where also nonlinear side conditions are imposed on the classes of admissi ble comparison functions. As special cases we include mappings whose range is forced to lie in some Riemannian manifold possibly with boundary or functions whose Jacobian is required to be strictly positive. The variational integrals under consideration are typically nonquadratic with respect to the gradient which immediately leads us to classes of degenerate elliptic systems. Let us mention some of the most important applications: - p-harmonic maps between Riemannian manifolds - systems of degenerate variational inequalities - model problems in nonlinear elasticity. Usually by working in appropriate Sobolev spaces, the existence of gener alized solutions is rather easy to establish (see [7]) but leads to apriori dis continuous functions. N� de r�f. du vendeur 9783528066239

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Topics in the Calculus of Variations

Martin Fuchs

Edit� par Vieweg+Teubner Verlag, Vieweg+Teubner Verlag Jan 1994, 1994

ISBN 10 : 3528066237 ISBN 13 : 9783528066239

Neuf Taschenbuch

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Taschenbuch. Etat : Neu. This item is printed on demand - Print on Demand Titel. Neuware -This report grew out of a series of lectures given at the East China Institute of Technology, Nanjing, during September 1992. The purpose of this book is to make beginning research students familiar with some problems in varia tional calculus which have been chosen following my personal taste but with the attempt to illustrate two basic principles in the calculus of variations which are the fundamental question of existence of (generalized) solutions and closely related the question of regularity. Chapter one is devoted to the study of variational integrals for vectorvalued functions which began with the pioneering work of Morrey [68] in the thirties. We concentrate on problems where also nonlinear side conditions are imposed on the classes of admissi ble comparison functions. As special cases we include mappings whose range is forced to lie in some Riemannian manifold possibly with boundary or functions whose Jacobian is required to be strictly positive. The variational integrals under consideration are typically nonquadratic with respect to the gradient which immediately leads us to classes of degenerate elliptic systems. Let us mention some of the most important applications: � p-harmonic maps between Riemannian manifolds � systems of degenerate variational inequalities � model problems in nonlinear elasticity. Usually by working in appropriate Sobolev spaces, the existence of gener alized solutions is rather easy to establish (see [7]) but leads to apriori dis continuous functions.Springer Vieweg in Springer Science + Business Media, Abraham-Lincoln-Stra�e 46, 65189 Wiesbaden 160 pp. Englisch. N� de r�f. du vendeur 9783528066239

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