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Author: Mariano Giaquinta
Publisher: Springer Science & Business Media
ISBN: 9783540640097
Category : Mathematics
Languages : en
Pages : 744
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Book Description
This monograph (in two volumes) deals with non scalar variational problems arising in geometry, as harmonic mappings between Riemannian manifolds and minimal graphs, and in physics, as stable equilibrium configuations in nonlinear elasticity or for liquid crystals. The presentation is selfcontained and accessible to non specialists. Topics are treated as far as possible in an elementary way, illustrating results with simple examples; in principle, chapters and even sections are readable independently of the general context, so that parts can be easily used for graduate courses. Open questions are often mentioned and the final section of each chapter discusses references to the literature and sometimes supplementary results. Finally, a detailed Table of Contents and an extensive Index are of help to consult this monograph
Author: Mariano Giaquinta
Publisher: Springer Science & Business Media
ISBN: 9783540640097
Category : Mathematics
Languages : en
Pages : 744
Get Book Here
Book Description
This monograph (in two volumes) deals with non scalar variational problems arising in geometry, as harmonic mappings between Riemannian manifolds and minimal graphs, and in physics, as stable equilibrium configuations in nonlinear elasticity or for liquid crystals. The presentation is selfcontained and accessible to non specialists. Topics are treated as far as possible in an elementary way, illustrating results with simple examples; in principle, chapters and even sections are readable independently of the general context, so that parts can be easily used for graduate courses. Open questions are often mentioned and the final section of each chapter discusses references to the literature and sometimes supplementary results. Finally, a detailed Table of Contents and an extensive Index are of help to consult this monograph
Author: Mariano Giaquinta
Publisher: Springer Science & Business Media
ISBN: 9783540640103
Category : Mathematics
Languages : en
Pages : 728
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Book Description
This monograph (in two volumes) deals with non scalar variational problems arising in geometry, as harmonic mappings between Riemannian manifolds and minimal graphs, and in physics, as stable equilibrium configuations in nonlinear elasticity or for liquid crystals. The presentation is selfcontained and accessible to non specialists. Topics are treated as far as possible in an elementary way, illustrating results with simple examples; in principle, chapters and even sections are readable independently of the general context, so that parts can be easily used for graduate courses. Open questions are often mentioned and the final section of each chapter discusses references to the literature and sometimes supplementary results. Finally, a detailed Table of Contents and an extensive Index are of help to consult this monograph
Author: Mariano Giaquinta
Publisher:
ISBN:
Category :
Languages : en
Pages : 697
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Book Description
Author: Mariano Giaquinta
Publisher: Springer Science & Business Media
ISBN: 3662062186
Category : Mathematics
Languages : en
Pages : 717
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Book Description
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.
Author: Mariano Giaquinta
Publisher:
ISBN:
Category : Calculus of variations
Languages : en
Pages :
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Book Description
Author: Stanley Alama
Publisher: American Mathematical Soc.
ISBN: 9780821873311
Category : Mathematics
Languages : en
Pages : 284
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Book Description
This book contains papers presented at the "Workshop on Singularities in PDE and the Calculus of Variations" at the CRM in July 2006. The main theme of the meeting was the formation of geometrical singularities in PDE problems with a variational formulation. These equations typically arise in some applications (to physics, engineering, or biology, for example) and their resolution often requires a combination of methods coming from areas such as functional and harmonic analysis, differential geometry and geometric measure theory. Among the PDE problems discussed were: the Cahn-Hilliard model of phase transitions and domain walls; vortices in Ginzburg-Landau type models for superconductivity and superfluidity; the Ohna-Kawasaki model for di-block copolymers; models of image enhancement; and Monge-Ampere functions. The articles give a sampling of problems and methods in this diverse area of mathematics, which touches a large part of modern mathematics and its applications.
Author: Luciano Carbone
Publisher: CRC Press
ISBN: 9781420035582
Category : Mathematics
Languages : en
Pages : 414
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Book Description
Over the last few decades, research in elastic-plastic torsion theory, electrostatic screening, and rubber-like nonlinear elastomers has pointed the way to some interesting new classes of minimum problems for energy functionals of the calculus of variations. This advanced-level monograph addresses these issues by developing the framework of a gener
Author: Gianni Dal Maso
Publisher: Birkhäuser
ISBN: 3034881932
Category : Mathematics
Languages : en
Pages : 195
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Book Description
This volume contains the Proceedings of the International Workshop Variational Methods For Discontinuous Structures, which was jointly organized by the Dipar timento di Matematica Francesco Brioschi of Milano Politecnico and the Interna tional School for Advanced Studies (SISSA) of Trieste. The Conference took place at Villa Erba Antica (Cernobbio) on the Lago di Como on July 4- 6, 2001. In past years the calculus of variations faced mainly the study of continuous structures, say particularly problems with smooth solutions. One of the deepest and more delicate problems was the regularity of weak solutions. More recently, new sophisticated tools have been introduced in order to study discontinuities: in many variational problems solutions develop singularities, and sometimes the most interesting part of a solution is the singularity itself. The conference intended to focus on recent developments in this direction. Some of the talks were devoted to differential or variational modelling of image segmentation, occlusion and textures synthesizing in image analysis, varia tional description of micro-magnetic materials, dimension reduction and structured deformations in elasticity and plasticity, phase transitions, irrigation and drainage, evolution of crystalline shapes; in most cases theoretical and numerical analysis of these models were provided. viii Preface Other talks were dedicated to specific problems of the calculus of variations: variational theory of weak or lower-dimensional structures, optimal transport prob lems with free Dirichlet regions, higher order variational problems, symmetrization in the BV framework.
Author: Michael Bildhauer
Publisher: Springer
ISBN: 3540448853
Category : Mathematics
Languages : en
Pages : 222
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Book Description
The author emphasizes a non-uniform ellipticity condition as the main approach to regularity theory for solutions of convex variational problems with different types of non-standard growth conditions. This volume first focuses on elliptic variational problems with linear growth conditions. Here the notion of a "solution" is not obvious and the point of view has to be changed several times in order to get some deeper insight. Then the smoothness properties of solutions to convex anisotropic variational problems with superlinear growth are studied. In spite of the fundamental differences, a non-uniform ellipticity condition serves as the main tool towards a unified view of the regularity theory for both kinds of problems.
Author: Michael Bildhauer
Publisher: Springer Science & Business Media
ISBN: 9783540402985
Category : Mathematics
Languages : en
Pages : 232
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Book Description
The author emphasizes a non-uniform ellipticity condition as the main approach to regularity theory for solutions of convex variational problems with different types of non-standard growth conditions. This volume first focuses on elliptic variational problems with linear growth conditions. Here the notion of a "solution" is not obvious and the point of view has to be changed several times in order to get some deeper insight. Then the smoothness properties of solutions to convex anisotropic variational problems with superlinear growth are studied. In spite of the fundamental differences, a non-uniform ellipticity condition serves as the main tool towards a unified view of the regularity theory for both kinds of problems.
