Singularities In Pde And The Calculus Of Variations

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Singularities In Pde And The Calculus Of Variations

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Author : Stanley Alama
language : en
Publisher: American Mathematical Soc.
Release Date :

Singularities In Pde And The Calculus Of Variations written by Stanley Alama and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.

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.

Singularities In Pde And The Calculus Of Variations

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Author :
language : en
Publisher:
Release Date : 2008

Singularities In Pde And The Calculus Of Variations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Calculus of variations categories.

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.

Calculus Of Variations

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Author : Filip Rindler
language : en
Publisher: Springer
Release Date : 2018-06-20

Calculus Of Variations written by Filip Rindler and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-20 with Mathematics categories.

This textbook provides a comprehensive introduction to the classical and modern calculus of variations, serving as a useful reference to advanced undergraduate and graduate students as well as researchers in the field. Starting from ten motivational examples, the book begins with the most important aspects of the classical theory, including the Direct Method, the Euler-Lagrange equation, Lagrange multipliers, Noether’s Theorem and some regularity theory. Based on the efficient Young measure approach, the author then discusses the vectorial theory of integral functionals, including quasiconvexity, polyconvexity, and relaxation. In the second part, more recent material such as rigidity in differential inclusions, microstructure, convex integration, singularities in measures, functionals defined on functions of bounded variation (BV), and Γ-convergence for phase transitions and homogenization are explored. While predominantly designed as a textbook for lecture courses on the calculus of variations, this book can also serve as the basis for a reading seminar or as a companion for self-study. The reader is assumed to be familiar with basic vector analysis, functional analysis, Sobolev spaces, and measure theory, though most of the preliminaries are also recalled in the appendix.

Partial Differential Equations And Calculus Of Variations

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Author : Stefan Hildebrandt
language : en
Publisher: Springer
Release Date : 2006-11-14

Partial Differential Equations And Calculus Of Variations written by Stefan Hildebrandt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

This volume contains 18 invited papers by members and guests of the former Sonderforschungsbereich in Bonn (SFB 72) who, over the years, collaborated on the research group "Solution of PDE's and Calculus of Variations". The emphasis is on existence and regularity results, on special equations of mathematical physics and on scattering theory.

Calculus Of Variations And Partial Differential Equations

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Author : Luigi Ambrosio
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Calculus Of Variations And Partial Differential Equations written by Luigi Ambrosio and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

At the summer school in Pisa in September 1996, Luigi Ambrosio and Norman Dancer each gave a course on the geometric problem of evolution of a surface by mean curvature, and degree theory with applications to PDEs respectively. This self-contained presentation accessible to PhD students bridged the gap between standard courses and advanced research on these topics. The resulting book is divided accordingly into 2 parts, and neatly illustrates the 2-way interaction of problems and methods. Each of the courses is augmented and complemented by additional short chapters by other authors describing current research problems and results.

Variational And Pde Methods In Nonlinear Science

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Author : Fabrice Bethuel
language : en
Publisher: Springer Nature
Release Date : 2025-07-01

Variational And Pde Methods In Nonlinear Science written by Fabrice Bethuel and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-01 with Mathematics categories.

This book presents three short courses on topics at the intersection of Calculus of Variations, PDEs and Material Science, based on lectures given at the CIME summer school “Variational and PDE Methods in Nonlinear Science”, held in Cetraro (Italy), July 10–14, 2023. Fabrice Bethuel discusses aympototics for Allen–Cahn systems, providing an overview of classical methods and tools for the scalar case and further results for the two-dimensional vectorial case. An alternate monotonicity formula is described, and the still open parabolic vectorial case is considered. Angkana Rüland considers the modelling and analysis of microstructures in shape-memory alloys, including material on quasiconvexity, differential inclusions, rigidity of the two-well problem under BV-regularity assumptions, and recent results on the quantitative dichotomy between rigidity and flexibility. Duvan Henao focuses on existence theory in nonlinear elasticity, where a central role is played by the Jacobian determinant. The methods developed have implications for the analysis of magnetoelasticity and nematic elastomers. The volume is aimed at graduate students and researchers interested in the applications of PDEs and the calculus of variations to the theory of phase transitions, fluid dynamics, materials science, and elasticity theory.

Calculus Of Variations And Geometric Evolution Problems

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Author : F. Bethuel
language : en
Publisher: Springer
Release Date : 2006-11-14

Calculus Of Variations And Geometric Evolution Problems written by F. Bethuel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

The international summer school on Calculus of Variations and Geometric Evolution Problems was held at Cetraro, Italy, 1996. The contributions to this volume reflect quite closely the lectures given at Cetraro which have provided an image of a fairly broad field in analysis where in recent years we have seen many important contributions. Among the topics treated in the courses were variational methods for Ginzburg-Landau equations, variational models for microstructure and phase transitions, a variational treatment of the Plateau problem for surfaces of prescribed mean curvature in Riemannian manifolds - both from the classical point of view and in the setting of geometric measure theory.

Symbolic Dynamics For Nonuniformly Hyperbolic Maps With Singularities In High Dimension

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Author : Ermerson Araujo
language : en
Publisher: American Mathematical Society
Release Date : 2024-10-23

Symbolic Dynamics For Nonuniformly Hyperbolic Maps With Singularities In High Dimension written by Ermerson Araujo and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-23 with Mathematics categories.

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Selected Works Of Frederick J Almgren Jr

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Author : Frederick J. Almgren
language : en
Publisher: American Mathematical Soc.
Release Date : 1999

Selected Works Of Frederick J Almgren Jr written by Frederick J. Almgren and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.

This volume offers a unique collection of some of the work of Frederick J. Almgren, Jr., the man most noted for defining the shape of geometric variational problems and for his role in founding The Geometry Center. Included in the volume are the following: a summary by Sheldon Chang of the famous 1700 page paper on singular sets of area-minimizing $m$-dimensional surfaces in $R^n$, a detailed summary by Brian White of Almgren's contributions to mathematics, his own announcements of several longer papers, important shorter papers, and memorable expository papers.Almgren's enthusiasm for the subject and his ability to locate mathematically beautiful problems that were 'ready to be solved' attracted many students who further expanded the subject into new areas. Many of these former students are now known for the clarity of their expositions and for the beauty of the problems that they work on. As Almgren's former graduate student, wife, and colleague, Professor Taylor has compiled an important volume on an extraordinary mathematician. This collection presents a fine comprehensive view of the man's mathematical legacy.

Sharp Boundary Trace Theory And Schr Dinger Operators On Bounded Lipschitz Domains

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Author : Jussi Behrndt
language : en
Publisher: American Mathematical Society
Release Date : 2025-04-02

Sharp Boundary Trace Theory And Schr Dinger Operators On Bounded Lipschitz Domains written by Jussi Behrndt and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-02 with Mathematics categories.

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