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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.
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About the Author
Prof. Dr. Martin Fuchs ist an der Universität des Saarlandes im Bereich Variationsrechnung und partielle Differentialgleichungen mit Bezügen zur mathematischen Physik und Differentialgeometrie tätig.
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- PublisherVieweg+Teubner Verlag
- Publication date1994
- ISBN 10 3528066237
- ISBN 13 9783528066239
- BindingPaperback
- LanguageEnglish
- Number of pages155
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Topics in the Calculus of Variations
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Topics in the Calculus of Variations (Advanced Lectures in Mathematics)
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Condition: 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. Seller Inventory # 4866977
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Topics in the Calculus of Variations
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Taschenbuch. Condition: 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. Seller Inventory # 9783528066239
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Topics in the Calculus of Variations
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Taschenbuch. Condition: 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. 148 pp. Englisch. Seller Inventory # 9783528066239
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Topics in the Calculus of Variations
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Taschenbuch. Condition: 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-Straße 46, 65189 Wiesbaden 160 pp. Englisch. Seller Inventory # 9783528066239
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Topics in the Calculus of Variations
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Topics in the Calculus of Variations (Advanced Lectures in Mathematics)
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ISBN 13: 9783528066239
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