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Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics Cartesian Currents in the Calculus of Variations

Cartesian Currents in the Calculus of Variations II

Variational Integrals

Authors: Giaquinta, Mariano, Modica, Guiseppe, Soucek, Jiri

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About this book

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.

Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook $189.00
price for USA in USD
  • ISBN 978-3-662-06218-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $249.99
price for USA in USD
  • ISBN 978-3-540-64010-3
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Softcover $249.99
price for USA in USD
  • ISBN 978-3-642-08375-4
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Cartesian Currents in the Calculus of Variations II
Book Subtitle
Variational Integrals
Authors
Series Title
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Series Volume
38
Copyright
1998
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-06218-0
DOI
10.1007/978-3-662-06218-0
Hardcover ISBN
978-3-540-64010-3
Softcover ISBN
978-3-642-08375-4
Series ISSN
0071-1136
Edition Number
1
Number of Pages
XXIV, 700
Topics