Cartesian Currents in the Calculus of Variations II: Variational Integrals
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1998
|
| Schriftenreihe: | Ergebnisse der Mathematik und ihrer Grenzgebiete / 3. Folge. A Series of Modern Surveys in Mathematics
38 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 |
| Beschreibung: | 1 Online-Ressource (XXIV, 700 p) |
| ISBN: | 9783662062180 9783642083754 |
| ISSN: | 0071-1136 |
| DOI: | 10.1007/978-3-662-06218-0 |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-06218-0 |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662062180 9783642083754 |
| issn | 0071-1136 |
| language | English |
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| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete / 3. Folge. A Series of Modern Surveys in Mathematics |
| spelling | Giaquinta, Mariano Verfasser aut Cartesian Currents in the Calculus of Variations II Variational Integrals by Mariano Giaquinta, Giuseppe Modica, Jiří Souček Berlin, Heidelberg Springer Berlin Heidelberg 1998 1 Online-Ressource (XXIV, 700 p) txt rdacontent c rdamedia cr rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete / 3. Folge. A Series of Modern Surveys in Mathematics 38 0071-1136 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 Mathematics Global analysis (Mathematics) Geometry Analysis Theoretical, Mathematical and Computational Physics Mathematik Modica, Giuseppe Sonstige oth Souček, Jiří Sonstige oth https://doi.org/10.1007/978-3-662-06218-0 Verlag Volltext |
| spellingShingle | Giaquinta, Mariano Cartesian Currents in the Calculus of Variations II Variational Integrals Mathematics Global analysis (Mathematics) Geometry Analysis Theoretical, Mathematical and Computational Physics Mathematik |
| title | Cartesian Currents in the Calculus of Variations II Variational Integrals |
| title_auth | Cartesian Currents in the Calculus of Variations II Variational Integrals |
| title_exact_search | Cartesian Currents in the Calculus of Variations II Variational Integrals |
| title_full | Cartesian Currents in the Calculus of Variations II Variational Integrals by Mariano Giaquinta, Giuseppe Modica, Jiří Souček |
| title_fullStr | Cartesian Currents in the Calculus of Variations II Variational Integrals by Mariano Giaquinta, Giuseppe Modica, Jiří Souček |
| title_full_unstemmed | Cartesian Currents in the Calculus of Variations II Variational Integrals by Mariano Giaquinta, Giuseppe Modica, Jiří Souček |
| title_short | Cartesian Currents in the Calculus of Variations II |
| title_sort | cartesian currents in the calculus of variations ii variational integrals |
| title_sub | Variational Integrals |
| topic | Mathematics Global analysis (Mathematics) Geometry Analysis Theoretical, Mathematical and Computational Physics Mathematik |
| topic_facet | Mathematics Global analysis (Mathematics) Geometry Analysis Theoretical, Mathematical and Computational Physics Mathematik |
| url | https://doi.org/10.1007/978-3-662-06218-0 |
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