| Dewey Class |
515.64 |
| Title |
Cartesian Currents in the Calculus of Variations II ([EBook]) : Variational Integrals / by Mariano Giaquinta, Giuseppe Modica, Jiří Souček. |
| Author |
Giaquinta, Mariano. , 1947- |
| Added Personal Name |
Modica, Giuseppe author. |
| Souček, Jiří author. |
| Other name(s) |
SpringerLink (Online service) |
| Publication |
Berlin, Heidelberg : Springer , 1998. |
| Physical Details |
XXIV, 700 pages : online resource. |
| Series |
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics 0071-1136 ; ; 38 |
| ISBN |
9783662062180 |
| Summary Note |
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.: |
| Contents note |
1. Regular Variational Integrals -- 2. Finite Elasticity and Weak Diffeomorphisms -- 3. The Dirichlet Integral in Sobolev Spaces -- 4. The Dirichlet Energy for Maps into S2 -- 5. Some Regular and Non Regular Variational Problems -- 6. The Non Parametric Area Functional -- Symbols. |
| System details note |
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users) |
| Internet Site |
http://dx.doi.org/10.1007/978-3-662-06218-0 |
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