Singularities In Pde And The Calculus Of Variations

Author : Stanley Alama,Lia Bronsard,Peter J. Sternberg
Publisher : American Mathematical Soc.
Page : 284 pages
File Size : 49,9 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 0821873318

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Singularities in PDE and the Calculus of Variations by Stanley Alama,Lia Bronsard,Peter J. Sternberg Pdf

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 : Stanley Alama,Lia Bronsard,Peter J. Sternberg
Publisher : American Mathematical Soc.
Page : 267 pages
File Size : 41,8 Mb
Release : 2008
Category : Mathematics
ISBN : 0821843508

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Singularities in PDE and the Calculus of Variations by Stanley Alama,Lia Bronsard,Peter J. Sternberg Pdf

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 : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 54,6 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 9789814464994

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Analysis of Singularities for Partial Differential Equations by Anonim Pdf

Author : Filip Rindler
Publisher : Springer
Page : 444 pages
File Size : 55,7 Mb
Release : 2018-06-20
Category : Mathematics
ISBN : 9783319776378

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Calculus of Variations by Filip Rindler Pdf

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.

Author : Stefan Hildebrandt,Rolf Leis
Publisher : Springer
Page : 433 pages
File Size : 55,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540460244

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Partial Differential Equations and Calculus of Variations by Stefan Hildebrandt,Rolf Leis Pdf

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.

Author : Serena Dipierro
Publisher : Springer
Page : 502 pages
File Size : 45,6 Mb
Release : 2019-07-12
Category : Mathematics
ISBN : 9783030189211

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Contemporary Research in Elliptic PDEs and Related Topics by Serena Dipierro Pdf

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.

Author : Stefan Hildebrandt,David Kinderlehrer
Publisher : Lecture Notes in Mathematics
Page : 324 pages
File Size : 45,5 Mb
Release : 1988-08
Category : Mathematics
ISBN : STANFORD:36105032430378

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Calculus of Variations and Partial Differential Equations by Stefan Hildebrandt,David Kinderlehrer Pdf

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.

Author : Martin F. Bach
Publisher : Birkhäuser
Page : 162 pages
File Size : 46,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034886871

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Variational Problems with Concentration by Martin F. Bach Pdf

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.

Author : C Bandle,Michel Chipot,J Saint Jean Paulin,Josef Bemelmans,I Shafrir
Publisher : CRC Press
Page : 300 pages
File Size : 50,7 Mb
Release : 1995-04-26
Category : Mathematics
ISBN : 0582239621

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Calculus of Variations, Applications and Computations by C Bandle,Michel Chipot,J Saint Jean Paulin,Josef Bemelmans,I Shafrir Pdf

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.

Author : Luigi Ambrosio,Norman Dancer
Publisher : Springer Science & Business Media
Page : 364 pages
File Size : 53,5 Mb
Release : 2000-01-24
Category : Mathematics
ISBN : 3540648038

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Calculus of Variations and Partial Differential Equations by Luigi Ambrosio,Norman Dancer Pdf

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.

Author : Ole Fogh Olsen,Luc Florack,Arjan Kuijper
Publisher : Springer
Page : 259 pages
File Size : 48,9 Mb
Release : 2005-12-04
Category : Computers
ISBN : 9783540320975

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Deep Structure, Singularities, and Computer Vision by Ole Fogh Olsen,Luc Florack,Arjan Kuijper Pdf

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.

Author : Nam Q. Le
Publisher : American Mathematical Society
Page : 599 pages
File Size : 51,6 Mb
Release : 2024-03-08
Category : Mathematics
ISBN : 9781470476250

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Analysis of Monge–Ampère Equations by Nam Q. Le Pdf

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.

Author : Anand P. Patel,Ashvin A. Swaminathan
Publisher : American Mathematical Society
Page : 114 pages
File Size : 50,7 Mb
Release : 2023-02-13
Category : Mathematics
ISBN : 9781470461577

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Inflectionary Invariants for Isolated Complete Intersection Curve Singularities by Anand P. Patel,Ashvin A. Swaminathan Pdf

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Author : Galia Devora Dafni,Robert John McCann,Alina Stancu
Publisher : American Mathematical Soc.
Page : 241 pages
File Size : 55,8 Mb
Release : 2013
Category : Mathematics
ISBN : 9780821894187

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Analysis and Geometry of Metric Measure Spaces by Galia Devora Dafni,Robert John McCann,Alina Stancu Pdf

Contains lecture notes from most of the courses presented at the 50th anniversary edition of the Seminaire de Mathematiques Superieure in Montreal. This 2011 summer school was devoted to the analysis and geometry of metric measure spaces, and featured much interplay between this subject and the emergent topic of optimal transportation.

Author : Andre Boivin,Javad Mashreghi
Publisher : American Mathematical Soc.
Page : 347 pages
File Size : 42,9 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821891735

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Complex Analysis and Potential Theory by Andre Boivin,Javad Mashreghi Pdf

This is the proceedings volume of an international conference entitled Complex Analysis and Potential Theory, which was held to honor the important contributions of two influential analysts, Kohur N. GowriSankaran and Paul M. Gauthier, in June 2011 at the Centre de Recherches Mathematiques (CRM) in Montreal. More than fifty mathematicians from fifteen countries participated in the conference. The twenty-four surveys and research articles contained in this book are based on the lectures given by some of the most established specialists in the fields. They reflect the wide breadth of research interests of the two honorees: from potential theory on trees to approximation on Riemann surfaces, from universality to inner and outer functions and the disc algebra, from branching processes to harmonic extension and capacities, from harmonic mappings and the Harnack principle to integration formulae in $\mathbb {C}^n$ and the Hartogs phenomenon, from fine harmonicity and plurisubharmonic functions to the binomial identity and the Riemann hypothesis, and more. This volume will be a valuable resource for specialists, young researchers, and graduate students from both fields, complex analysis and potential theory. It will foster further cooperation and the exchange of ideas and techniques to find new research perspectives.