Singularities In Pde And The Calculus Of Variations

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Singularities in PDE and the Calculus of Variations

Author : Stanley Alama
Publisher : American Mathematical Soc.
ISBN 13 : 9780821873311
Total Pages : 284 pages
Book Rating : 4.8/5 (733 download)

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Book Synopsis Singularities in PDE and the Calculus of Variations by : Stanley Alama

Download or read book Singularities in PDE and the Calculus of Variations written by Stanley Alama and published by American Mathematical Soc.. This book was released on with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Stanley Alama
Publisher : American Mathematical Soc.
ISBN 13 : 9780821843505
Total Pages : 267 pages
Book Rating : 4.8/5 (435 download)

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Book Synopsis Singularities in PDE and the Calculus of Variations by : Stanley Alama

Download or read book Singularities in PDE and the Calculus of Variations written by Stanley Alama and published by American Mathematical Soc.. This book was released on 2008 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Analysis of Singularities for Partial Differential Equations

Author :
Publisher :
ISBN 13 : 9814464996
Total Pages : pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Analysis of Singularities for Partial Differential Equations by :

Download or read book Analysis of Singularities for Partial Differential Equations written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Calculus of Variations

Author : Filip Rindler
Publisher : Springer
ISBN 13 : 3319776371
Total Pages : 444 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Calculus of Variations by : Filip Rindler

Download or read book Calculus of Variations written by Filip Rindler and published by Springer. This book was released on 2018-06-20 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Stefan Hildebrandt
Publisher : Springer
ISBN 13 : 3540460241
Total Pages : 433 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Partial Differential Equations and Calculus of Variations by : Stefan Hildebrandt

Download or read book Partial Differential Equations and Calculus of Variations written by Stefan Hildebrandt and published by Springer. This book was released on 2006-11-14 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Contemporary Research in Elliptic PDEs and Related Topics

Author : Serena Dipierro
Publisher : Springer
ISBN 13 : 303018921X
Total Pages : 502 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Contemporary Research in Elliptic PDEs and Related Topics by : Serena Dipierro

Download or read book Contemporary Research in Elliptic PDEs and Related Topics written by Serena Dipierro and published by Springer. This book was released on 2019-07-12 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects contributions from the speakers at an INdAM Intensive period held at the University of Bari in 2017. The contributions cover several aspects of partial differential equations whose development in recent years has experienced major breakthroughs in terms of both theory and applications. The topics covered include nonlocal equations, elliptic equations and systems, fully nonlinear equations, nonlinear parabolic equations, overdetermined boundary value problems, maximum principles, geometric analysis, control theory, mean field games, and bio-mathematics. The authors are trailblazers in these topics and present their work in a way that is exhaustive and clearly accessible to PhD students and early career researcher. As such, the book offers an excellent introduction to a variety of fundamental topics of contemporary investigation and inspires novel and high-quality research.

Calculus of Variations and Partial Differential Equations

Author : Stefan Hildebrandt
Publisher : Lecture Notes in Mathematics
ISBN 13 :
Total Pages : 324 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Calculus of Variations and Partial Differential Equations by : Stefan Hildebrandt

Download or read book Calculus of Variations and Partial Differential Equations written by Stefan Hildebrandt and published by Lecture Notes in Mathematics. This book was released on 1988-08 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the contents: A. Arosio: Global solvability of second order evolution equations in Banach scales.- H. Beirao da Veiga: On the incompressible limit of the compressible Navier-Stokes equations.- A. Bove: Propagation of singularities for hyperbolic operators with double characteristics.- G. Buttazzo: Relaxation problems in control theory.- R. Finn: The inclination of an H-graph.- P.R. Garabedian: On the mathematical theory of vortex sheets.- N. Garofalo: New estimates of the fundamental solution and Wiener's criterion for parabolic equations with variable coefficients.- M.G. Garroni: Green function and invariant density for an integro-differential operator.- M. Giaquinta: Some remarks on the regularity of minimizers.- E. Giusti: Quadratic functionals with splitting coefficients.- R. Gulliver: Minimal surfaces on finite index in manifolds of positive scalar curvature.- R. Hardt, D. Kinderlehrer, M. Luskin: Remarks about the mathematical theory of liquid crystals.- E. Heinz: On quasi-minimal surfaces.- P. Laurence, E. Stredulinsky: A survey of recent regularity results for second order queer differential equations.- C.-S. Lin, W.-M. Ni: On the diffusion coefficient of a semilinear Neumann problem.- M. Longinetti: Some isoperimetric inequalities for the level curves of capacity and Green's functions on convex plane domains.- P. Marcati: Nonhomogeneous quasilinear hyperbolic systems: initial and boundary value problem.- E. Mascolo: Existence results for non convex problems of the calculus of variations.- U. Mosco: Wiener criteria and variational convergences.- L. Nirenberg: Fully nonlinear second order elliptic equations.- J. Serrin: Positive solutions of a prescribed mean curvature problem.- D. Socolescu: On the convergence at infinity of solutions with finite Dirichlet integral to the exterior Dirichlet problem for the steady plane Navier-Stokes system of equations.- J. Spruck: The elliptic Sinh Gordon equation and the construction of toroidal soap bubbles.

Calculus of Variations and Partial Differential Equations

Author : Luigi Ambrosio
Publisher : Springer Science & Business Media
ISBN 13 : 9783540648031
Total Pages : 364 pages
Book Rating : 4.6/5 (48 download)

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Book Synopsis Calculus of Variations and Partial Differential Equations by : Luigi Ambrosio

Download or read book Calculus of Variations and Partial Differential Equations written by Luigi Ambrosio and published by Springer Science & Business Media. This book was released on 2000-01-24 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Problems with Concentration

Author : Martin F. Bach
Publisher : Birkhäuser
ISBN 13 : 303488687X
Total Pages : 162 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Variational Problems with Concentration by : Martin F. Bach

Download or read book Variational Problems with Concentration written by Martin F. Bach and published by Birkhäuser. This book was released on 2012-12-06 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained research monograph focuses on semilinear Dirichlet problems and similar equations involving the p-Laplacian. The author explains new techniques in detail, and derives several numerical methods approximating the concentration point and the free boundary. The corresponding plots are highlights of this book.

Deep Structure, Singularities, and Computer Vision

Author : Ole Fogh Olsen
Publisher : Springer
ISBN 13 : 3540320970
Total Pages : 259 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Deep Structure, Singularities, and Computer Vision by : Ole Fogh Olsen

Download or read book Deep Structure, Singularities, and Computer Vision written by Ole Fogh Olsen and published by Springer. This book was released on 2005-12-04 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-proceedings of the First International Workshop on Deep Structure, Singularities, and Computer Vision, DSSCV 2005, held in Maastricht, The Netherlands in June 2005. The 14 revised full papers and 8 revised poster papers presented were carefully reviewed and selected for inclusion in the book. They represent the current state-of-the-art in understanding the relation between structural, topological information represented by singularities and metric information of signals, shapes, images, and colors.

Analysis of Monge–Ampère Equations

Author : Nam Q. Le
Publisher : American Mathematical Society
ISBN 13 : 1470476258
Total Pages : 599 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Analysis of Monge–Ampère Equations by : Nam Q. Le

Download or read book Analysis of Monge–Ampère Equations written by Nam Q. Le and published by American Mathematical Society. This book was released on 2024-03-08 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic analysis of the Monge–Ampère equation, the linearized Monge–Ampère equation, and their applications, with emphasis on both interior and boundary theories. Starting from scratch, it gives an extensive survey of fundamental results, essential techniques, and intriguing phenomena in the solvability, geometry, and regularity of Monge–Ampère equations. It describes in depth diverse applications arising in geometry, fluid mechanics, meteorology, economics, and the calculus of variations. The modern treatment of boundary behaviors of solutions to Monge–Ampère equations, a very important topic of the theory, is thoroughly discussed. The book synthesizes many important recent advances, including Savin's boundary localization theorem, spectral theory, and interior and boundary regularity in Sobolev and Hölder spaces with optimal assumptions. It highlights geometric aspects of the theory and connections with adjacent research areas. This self-contained book provides the necessary background and techniques in convex geometry, real analysis, and partial differential equations, presents detailed proofs of all theorems, explains subtle constructions, and includes well over a hundred exercises. It can serve as an accessible text for graduate students as well as researchers interested in this subject.

Calculus of Variations, Applications and Computations

Author : C Bandle
Publisher : CRC Press
ISBN 13 : 9780582239623
Total Pages : 300 pages
Book Rating : 4.2/5 (396 download)

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Book Synopsis Calculus of Variations, Applications and Computations by : C Bandle

Download or read book Calculus of Variations, Applications and Computations written by C Bandle and published by CRC Press. This book was released on 1995-04-26 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research presents some important domains of partial differential equations and applied mathematics including calculus of variations, control theory, modelling, numerical analysis and various applications in physics, mechanics and engineering. These topics are now part of many areas of science and have experienced tremendous development during the last decades.

Nonlinear Analysis and Optimization

Author : Boris S. Mordukhovich
Publisher : American Mathematical Soc.
ISBN 13 : 1470417367
Total Pages : 320 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Nonlinear Analysis and Optimization by : Boris S. Mordukhovich

Download or read book Nonlinear Analysis and Optimization written by Boris S. Mordukhovich and published by American Mathematical Soc.. This book was released on 2016-02-26 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the IMU/AMS Special Session on Nonlinear Analysis and Optimization, held from June 16-19, 2014, at the Second Joint International Meeting of the Israel Mathematical Union (IMU) and the American Mathematical Society (AMS), Bar-Ilan and Tel-Aviv Universities, Israel, and the Workshop on Nonlinear Analysis and Optimization, held on June 12, 2014, at the Technion-Israel Institute of Technology. The papers in this volume cover many different topics in Nonlinear Analysis and Optimization, including: Taylor domination property for analytic functions in the complex disk, mappings with upper integral bounds for p -moduli, multiple Fourier transforms and trigonometric series in line with Hardy's variation, finite-parameter feedback control for stabilizing damped nonlinear wave equations, implicit Euler approximation and optimization of one-sided Lipschitz differential inclusions, Bolza variational problems with extended-valued integrands on large intervals, first order singular variational problem with nonconvex cost, gradient and extragradient methods for the elasticity imaging inverse problem, discrete approximations of the entropy functional for probability measures on the plane, optimal irrigation scheduling for wheat production, existence of a fixed point of nonexpansive mappings in uniformly convex Banach spaces, strong convergence properties of m-accretive bounded operators, the Reich-Simons convex analytic inequality, nonlinear input-output equilibrium, differential linear-quadratic Nash games with mixed state-control constraints, and excessive revenue models of competitive markets.

Partial Differential Equations

Author : Walter A. Strauss
Publisher : John Wiley & Sons
ISBN 13 : 0470054565
Total Pages : 467 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Partial Differential Equations by : Walter A. Strauss

Download or read book Partial Differential Equations written by Walter A. Strauss and published by John Wiley & Sons. This book was released on 2007-12-21 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.

Geometric Partial Differential Equations

Author : Antonin Chambolle
Publisher : Springer Science & Business Media
ISBN 13 : 8876424733
Total Pages : 400 pages
Book Rating : 4.8/5 (764 download)

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Book Synopsis Geometric Partial Differential Equations by : Antonin Chambolle

Download or read book Geometric Partial Differential Equations written by Antonin Chambolle and published by Springer Science & Business Media. This book was released on 2014-01-17 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the outcome of a conference held at the Centro De Giorgi of the Scuola Normale of Pisa in September 2012. The aim of the conference was to discuss recent results on nonlinear partial differential equations, and more specifically geometric evolutions and reaction-diffusion equations. Particular attention was paid to self-similar solutions, such as solitons and travelling waves, asymptotic behaviour, formation of singularities and qualitative properties of solutions. These problems arise in many models from Physics, Biology, Image Processing and Applied Mathematics in general, and have attracted a lot of attention in recent years.

Inflectionary Invariants for Isolated Complete Intersection Curve Singularities

Author : Anand P. Patel
Publisher : American Mathematical Society
ISBN 13 : 1470461579
Total Pages : 114 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Inflectionary Invariants for Isolated Complete Intersection Curve Singularities by : Anand P. Patel

Download or read book Inflectionary Invariants for Isolated Complete Intersection Curve Singularities written by Anand P. Patel and published by American Mathematical Society. This book was released on 2023-02-13 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Cartesian Currents in the Calculus of Variations II

Author : Mariano Giaquinta
Publisher : Springer Science & Business Media
ISBN 13 : 3662062186
Total Pages : 717 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Cartesian Currents in the Calculus of Variations II by : Mariano Giaquinta

Download or read book Cartesian Currents in the Calculus of Variations II written by Mariano Giaquinta and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 717 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.