Download or read book Unstable solutions of two dimensional geometric variational problems written by Jürgen Jost and published by . This book was released on 1991 with total page 49 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Variational Methods written by BERESTYCKI and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the framework of the "Annee non lineaire" (the special nonlinear year) sponsored by the C.N.R.S. (the French National Center for Scien tific Research), a meeting was held in Paris in June 1988. It took place in the Conference Hall of the Ministere de la Recherche and had as an organizing theme the topic of "Variational Problems." Nonlinear analysis has been one of the leading themes in mathemat ical research for the past decade. The use of direct variational methods has been particularly successful in understanding problems arising from physics and geometry. The growth of nonlinear analysis is largely due to the wealth of ap plications from various domains of sciences and industrial applica tions. Most of the papers gathered in this volume have their origin in applications: from mechanics, the study of Hamiltonian systems, from physics, from the recent mathematical theory of liquid crystals, from geometry, relativity, etc. Clearly, no single volume could pretend to cover the whole scope of nonlinear variational problems. We have chosen to concentrate on three main aspects of these problems, organizing them roughly around the following topics: 1. Variational methods in partial differential equations in mathemat ical physics 2. Variational problems in geometry 3. Hamiltonian systems and related topics.
Download or read book Riemannian Geometry and Geometric Analysis written by Jürgen Jost and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: FROM REVIEWS OF THE FIRST EDITION "a very readable introduction to Riemannian geometry...it is most welcome...The book is made more interesting by the perspectives in various sections, where the author mentions the history and development of the material and provides the reader with references."-MATHEMATICAL REVIEWS
Download or read book Differential Geometry Partial Differential Equations on Manifolds written by Robert Everist Greene and published by American Mathematical Soc.. This book was released on 1993 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first of three parts comprising Volume 54, the proceedings of the Summer Research Institute on Differential Geometry, held at the University of California, Los Angeles, July 1990 (ISBN for the set is 0-8218-1493-1). Part 1 begins with a problem list by S.T. Yau, successor to his 1980 list ( Sem
Download or read book Handbook of Global Analysis written by Demeter Krupka and published by Elsevier. This book was released on 2011-08-11 with total page 1243 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive exposition of topics covered by the American Mathematical Society’s classification “Global Analysis , dealing with modern developments in calculus expressed using abstract terminology. It will be invaluable for graduate students and researchers embarking on advanced studies in mathematics and mathematical physics.This book provides a comprehensive coverage of modern global analysis and geometrical mathematical physics, dealing with topics such as; structures on manifolds, pseudogroups, Lie groupoids, and global Finsler geometry; the topology of manifolds and differentiable mappings; differential equations (including ODEs, differential systems and distributions, and spectral theory); variational theory on manifolds, with applications to physics; function spaces on manifolds; jets, natural bundles and generalizations; and non-commutative geometry. - Comprehensive coverage of modern global analysis and geometrical mathematical physics- Written by world-experts in the field- Up-to-date contents
Download or read book Two Dimensional Geometric Variational Problems written by Jürgen Jost and published by . This book was released on 1991-03-29 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph treats variational problems for mappings from a surface equipped with a conformal structure into Euclidean space or a Riemannian manifold. Presents a general theory of such variational problems, proving existence and regularity theorems with particular conceptual emphasis on the geometric aspects of the theory and thorough investigation of the connections with complex analysis. Among the topics covered are: Plateau's problem, the regularity theory of solutions, a variational approach for obtaining various conformal representation theorems, a general existence theorem for harmonic mappings, and a new approach to Teichmuller theory via harmonic maps.
Download or read book Calculus of Variations and Geometric Evolution Problems written by F. Bethuel and published by Springer. This book was released on 2006-11-14 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Differential Geometry Riemannian Geometry written by Robert Everist Greene and published by American Mathematical Soc.. This book was released on 1993 with total page 735 pages. Available in PDF, EPUB and Kindle. Book excerpt: The third of three parts comprising Volume 54, the proceedings of the Summer Research Institute on Differential Geometry, held at the University of California, Los Angeles, July 1990 (ISBN for the set is 0-8218-1493-1). Part 3 begins with an overview by R.E. Greene of some recent trends in Riemannia
Download or read book Handbook of Geometric Analysis written by Lizhen Ji and published by . This book was released on 2008 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Geometric Analysis combines differential equations with differential geometry. An important aspect of geometric analysis is to approach geometric problems by studying differential equations. Besides some known linear differential operators such as the Laplace operator, many differential equations arising from differential geometry are nonlinear. A particularly important example is the Monge-Amperè equation. Applications to geometric problems have also motivated new methods and techniques in differential equations. The field of geometric analysis is broad and has had many striking applications. This handbook of geometric analysis--the first of the two to be published in the ALM series--presents introductions and survey papers treating important topics in geometric analysis, with their applications to related fields. It can be used as a reference by graduate students and by researchers in related areas."--Back cover.
Download or read book Variational Problems in Topology written by A.T. Fomenko and published by Routledge. This book was released on 2019-06-21 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many of the modern variational problems of topology arise in different but overlapping fields of scientific study: mechanics, physics and mathematics. In this work, Professor Fomenko offers a concise and clear explanation of some of these problems (both solved and unsolved), using current methods of analytical topology. His book falls into three interrelated sections. The first gives an elementary introduction to some of the most important concepts of topology used in modern physics and mechanics: homology and cohomology, and fibration. The second investigates the significant role of Morse theory in modern aspects of the topology of smooth manifolds, particularly those of three and four dimensions. The third discusses minimal surfaces and harmonic mappings, and presents a number of classic physical experiments that lie at the foundations of modern understanding of multidimensional variational calculus. The author's skilful exposition of these topics and his own graphic illustrations give an unusual motivation to the theory expounded, and his work is recommended reading for specialists and non-specialists alike, involved in the fields of physics and mathematics at both undergraduate and graduate levels.
Download or read book Geometric Analysis and the Calculus of Variations written by Stefan Hildebrandt and published by . This book was released on 1996 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to the ideas of Stefan Hildebrant, whose doctrinal students include Bernd Schmidt and Klaus Stefan. His solution to the boundry regularity question for minimal surfaces bounded by a pescribed Jordan curve brought him world fame.
Download or read book Differential Geometry Geometry in Mathematical Physics and Related Topics written by Robert Everist Greene and published by American Mathematical Soc.. This book was released on 1993 with total page 681 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second of three parts comprising Volume 54, the proceedings of the Summer Research Institute on Differential Geometry, held at the University of California, Los Angeles, July 1990 (ISBN for the set is 0-8218-1493-1). Among the subjects of Part 2 are gauge theory, symplectic geometry, complex ge
Download or read book Partial Differential Equations on Manifolds written by Robert Everist Greene and published by . This book was released on 1993 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book MEAN FIELD THEORIES AND DUAL VARIATION written by Takashi Suzuki and published by Springer Science & Business Media. This book was released on 2009-01-01 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: A mathematical theory is introduced in this book to unify a large class of nonlinear partial differential equation (PDE) models for better understanding and analysis of the physical and biological phenomena they represent. The so-called mean field approximation approach is adopted to describe the macroscopic phenomena from certain microscopic principles for this unified mathematical formulation. Two key ingredients for this approach are the notions of “duality” according to the PDE weak solutions and “hierarchy” for revealing the details of the otherwise hidden secrets, such as physical mystery hidden between particle density and field concentration, quantized blow up biological mechanism sealed in chemotaxis systems, as well as multi-scale mathematical explanations of the Smoluchowski–Poisson model in non-equilibrium thermodynamics, two-dimensional turbulence theory, self-dual gauge theory, and so forth. This book shows how and why many different nonlinear problems are inter-connected in terms of the properties of duality and scaling, and the way to analyze them mathematically.
Download or read book Introduction to Numerical Methods for Variational Problems written by Hans Petter Langtangen and published by Springer Nature. This book was released on 2019-09-26 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook teaches finite element methods from a computational point of view. It focuses on how to develop flexible computer programs with Python, a programming language in which a combination of symbolic and numerical tools is used to achieve an explicit and practical derivation of finite element algorithms. The finite element library FEniCS is used throughout the book, but the content is provided in sufficient detail to ensure that students with less mathematical background or mixed programming-language experience will equally benefit. All program examples are available on the Internet.
Download or read book Surveys in Differential Geometry written by Shing-Tung Yau and published by . This book was released on 2003 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt:
