Advanced Lectures in Mathematics

Topics in the Calculus of Variations

Authors: Fuchs, Martin

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About this book

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.

About the authors

Prof. Dr. Martin Fuchs ist an der Universität des Saarlandes im Bereich Variationsrechnung und partielle Differentialgleichungen mit Bezügen zur mathematischen Physik und Differentialgeometrie tätig.

Table of contents (2 chapters)

  • Degenerate Variational Integrals with Nonlinear Side Conditions, p-harmonic Maps and Related Topics

    Fuchs, Martin

    Pages 1-83

  • Manifolds of Prescribed Mean Curvature in the Setting of Geometric Measure Theory

    Fuchs, Martin

    Pages 84-138

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-322-86528-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $149.00
price for USA
  • ISBN 978-3-528-06623-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Topics in the Calculus of Variations
Authors
Series Title
Advanced Lectures in Mathematics
Copyright
1994
Publisher
Vieweg+Teubner Verlag
Copyright Holder
Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden
eBook ISBN
978-3-322-86528-1
DOI
10.1007/978-3-322-86528-1
Softcover ISBN
978-3-528-06623-9
Series ISSN
0932-7134
Edition Number
1
Number of Pages
VII, 148
Topics