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Plateaus Problem And The Calculus Of Variations
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Book Synopsis Plateau's Problem and the Calculus of Variations. (MN-35) by : Michael Struwe
Download or read book Plateau's Problem and the Calculus of Variations. (MN-35) written by Michael Struwe and published by Princeton University Press. This book was released on 2014-07-14 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is meant to give an account of recent developments in the theory of Plateau's problem for parametric minimal surfaces and surfaces of prescribed constant mean curvature ("H-surfaces") and its analytical framework. A comprehensive overview of the classical existence and regularity theory for disc-type minimal and H-surfaces is given and recent advances toward general structure theorems concerning the existence of multiple solutions are explored in full detail. The book focuses on the author's derivation of the Morse-inequalities and in particular the mountain-pass-lemma of Morse-Tompkins and Shiffman for minimal surfaces and the proof of the existence of large (unstable) H-surfaces (Rellich's conjecture) due to Brezis-Coron, Steffen, and the author. Many related results are covered as well. More than the geometric aspects of Plateau's problem (which have been exhaustively covered elsewhere), the author stresses the analytic side. The emphasis lies on the variational method. Originally published in 1989. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Book Synopsis The Problem of Plateau by : Themistocles M. Rassias
Download or read book The Problem of Plateau written by Themistocles M. Rassias and published by World Scientific. This book was released on 1992 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of papers written by eminent scientists from the international mathematical community, who present the latest information concerning the problem of Plateau after its classical solution by Jesse Douglas and Tibor Rad¢. The contributing papers provide insight and perspective on various problems in modern topics of Calculus of Variations, Global Differential Geometry and Global Nonlinear Analysis as related to the problem of Plateau.
Book Synopsis On the Problem of Plateau by : Tibor Radó
Download or read book On the Problem of Plateau written by Tibor Radó and published by Springer. This book was released on 2013-11-11 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most immediate one-dimensional variation problem is certainly the problem of determining an arc of curve, bounded by two given and having a smallest possible length. The problem of deter points mining and investigating a surface with given boundary and with a smallest possible area might then be considered as the most immediate two-dimensional variation problem. The classical work, concerned with the latter problem, is summed up in a beautiful and enthusiastic manner in DARBOUX'S Theorie generale des surfaces, vol. I, and in the first volume of the collected papers of H. A. SCHWARZ. The purpose of the present report is to give a picture of the progress achieved in this problem during the period beginning with the Thesis of LEBESGUE (1902). Our problem has always been considered as the outstanding example for the application of Analysis and Geometry to each other, and the recent work in the problem will certainly strengthen this opinion. It seems, in particular, that this recent work will be a source of inspiration to the Analyst interested in Calculus of Variations and to the Geometer interested in the theory of the area and in the theory of the conformal maps of general surfaces. These aspects of the subject will be especially emphasized in this report. The report consists of six Chapters. The first three Chapters are important tools or concerned with investigations which yielded either important ideas for the proofs of the existence theorems reviewed in the last three Chapters.
Book Synopsis Calculus of Variations and Geometric Evolution Problems by : F. Bethuel
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.
Book Synopsis Geometric Analysis and the Calculus of Variations by : Stefan Hildebrandt
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.
Book Synopsis Introduction To The Calculus Of Variations (3rd Edition) by : Bernard Dacorogna
Download or read book Introduction To The Calculus Of Variations (3rd Edition) written by Bernard Dacorogna and published by World Scientific Publishing Company. This book was released on 2014-08-13 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: The calculus of variations is one of the oldest subjects in mathematics, and it is very much alive and still evolving. Besides its mathematical importance and its links to other branches of mathematics, such as geometry or differential equations, it is widely used in physics, engineering, economics and biology.This book serves both as a guide to the expansive existing literature and as an aid to the non-specialist — mathematicians, physicists, engineers, students or researchers — in discovering the subject's most important problems, results and techniques. Despite the aim of addressing non-specialists, mathematical rigor has not been sacrificed; most of the theorems are either fully proved or proved under more stringent conditions.In this new edition, several new exercises have been added. The book, containing a total of 119 exercises with detailed solutions, is well designed for a course at both undergraduate and graduate levels.
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.
Book Synopsis The Problem Of Plateau: A Tribute To Jesse Douglas And Tibor Rado by : Themistocles M Rassias
Download or read book The Problem Of Plateau: A Tribute To Jesse Douglas And Tibor Rado written by Themistocles M Rassias and published by World Scientific. This book was released on 1992-12-21 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of papers written by eminent scientists from the international mathematical community, who present the latest information concerning the problem of Plateau after its classical solution by Jesse Douglas and Tibor Radó. The contributing papers provide insight and perspective on various problems in modern topics of Calculus of Variations, Global Differential Geometry and Global Nonlinear Analysis as related to the problem of Plateau.
Book Synopsis Variational Methods by : Michael Struwe
Download or read book Variational Methods written by Michael Struwe and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hilberts talk at the second International Congress of 1900 in Paris marked the beginning of a new era in the calculus of variations. A development began which, within a few decades, brought tremendous success, highlighted by the 1929 theorem of Ljusternik and Schnirelman on the existence of three distinct prime closed geodesics on any compact surface of genus zero, and the 1930/31 solution of Plateaus problem by Douglas and Rad. This third edition gives a concise introduction to variational methods and presents an overview of areas of current research in the field, plus a survey on new developments.
Book Synopsis Two-dimensional Problems of the Calculus of Variations by : A. G. Sigalov
Download or read book Two-dimensional Problems of the Calculus of Variations written by A. G. Sigalov and published by . This book was released on 1953 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Official Summary of Security Transactions and Holdings Reported to the Securities and Exchange Commission Under the Securities Exchange Act of 1934 and the Public Utility Holding Company Act of 1935 by :
Download or read book Official Summary of Security Transactions and Holdings Reported to the Securities and Exchange Commission Under the Securities Exchange Act of 1934 and the Public Utility Holding Company Act of 1935 written by and published by . This book was released on 1974 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometric Measure Theory and the Calculus of Variations by : William K. Allard
Download or read book Geometric Measure Theory and the Calculus of Variations written by William K. Allard and published by American Mathematical Soc.. This book was released on 1986 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes twenty-six papers that survey a cross section of work in modern geometric measure theory and its applications in the calculus of variations. This title provides an access to the material, including introductions and summaries of many of the authors' much longer works and a section containing 80 open problems in the field.
Book Synopsis Aspects of the Calculus of Variations by : Hans Lewy
Download or read book Aspects of the Calculus of Variations written by Hans Lewy and published by . This book was released on 1939 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 2012-12-06 with total page 347 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.
Book Synopsis Minimal Surfaces and Functions of Bounded Variation by : Giusti
Download or read book Minimal Surfaces and Functions of Bounded Variation written by Giusti and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of finding minimal surfaces, i. e. of finding the surface of least area among those bounded by a given curve, was one of the first considered after the foundation of the calculus of variations, and is one which received a satis factory solution only in recent years. Called the problem of Plateau, after the blind physicist who did beautiful experiments with soap films and bubbles, it has resisted the efforts of many mathematicians for more than a century. It was only in the thirties that a solution was given to the problem of Plateau in 3-dimensional Euclidean space, with the papers of Douglas [DJ] and Rado [R T1, 2]. The methods of Douglas and Rado were developed and extended in 3-dimensions by several authors, but none of the results was shown to hold even for minimal hypersurfaces in higher dimension, let alone surfaces of higher dimension and codimension. It was not until thirty years later that the problem of Plateau was successfully attacked in its full generality, by several authors using measure-theoretic methods; in particular see De Giorgi [DG1, 2, 4, 5], Reifenberg [RE], Federer and Fleming [FF] and Almgren [AF1, 2]. Federer and Fleming defined a k-dimensional surface in IR" as a k-current, i. e. a continuous linear functional on k-forms. Their method is treated in full detail in the splendid book of Federer [FH 1].
Book Synopsis On the Problem of Plateau / Subharmonic Functions by : T. Rado
Download or read book On the Problem of Plateau / Subharmonic Functions written by T. Rado and published by Springer. This book was released on 1971-01-04 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: A convex function f may be called sublinear in the following sense; if a linear function l is ::=: j at the boundary points of an interval, then l:> j in the interior of that interval also. If we replace the terms interval and linear junction by the terms domain and harmonic function, we obtain a statement which expresses the characteristic property of subharmonic functions of two or more variables. This ge neralization, formulated and developed by F. RIEsz, immediately at tracted the attention of many mathematicians, both on account of its intrinsic interest and on account of the wide range of its applications. If f (z) is an analytic function of the complex variable z = x + i y. then If (z) I is subharmonic. The potential of a negative mass-distribu tion is subharmonic. In differential geometry, surfaces of negative curvature and minimal surfaces can be characterized in terms of sub harmonic functions. The idea of a subharmonic function leads to significant applications and interpretations in the fields just referred to, and· conversely, every one of these fields is an apparently in exhaustible source of new theorems on subharmonic functions, either by analogy or by direct implication.
Book Synopsis Calculus of Variations I by : Mariano Giaquinta
Download or read book Calculus of Variations I written by Mariano Giaquinta and published by Springer Science & Business Media. This book was released on 2004-06-23 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume treatise is a standard reference in the field. It pays special attention to the historical aspects and the origins partly in applied problems—such as those of geometric optics—of parts of the theory. It contains an introduction to each chapter, section, and subsection and an overview of the relevant literature in the footnotes and bibliography. It also includes an index of the examples used throughout the book.
