Geometric Analysis and the Calculus of Variations PDF Download
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Author: Stefan Hildebrandt
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 426
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Book Description
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.
Author: Stefan Hildebrandt
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 426
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Book Description
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.
Author: Stefan Hildebrandt
Publisher: Springer Science & Business Media
ISBN: 3642556272
Category : Mathematics
Languages : en
Pages : 663
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Book Description
This book is not a textbook, but rather a coherent collection of papers from the field of partial differential equations. Nevertheless we believe that it may very well serve as a good introduction into some topics of this classical field of analysis which, despite of its long history, is highly modem and well prospering. Richard Courant wrote in 1950: "It has always been a temptationfor mathematicians to present the crystallized product of their thought as a deductive general theory and to relegate the individual mathematical phenomenon into the role of an example. The reader who submits to the dogmatic form will be easily indoctrinated. Enlightenment, however, must come from an understanding of motives; live mathematical development springs from specific natural problems which can be easily understood, but whose solutions are difficult and demand new methods or more general significance. " We think that many, if not all, papers of this book are written in this spirit and will give the reader access to an important branch of analysis by exhibiting interest ing problems worth to be studied. Most of the collected articles have an extensive introductory part describing the history of the presented problems as well as the state of the art and offer a well chosen guide to the literature. This way the papers became lengthier than customary these days, but the level of presentation is such that an advanced graduate student should find the various articles both readable and stimulating.
Author: William K. Allard
Publisher: American Mathematical Soc.
ISBN: 0821814702
Category : Mathematics
Languages : en
Pages : 482
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Book Description
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.
Author: Fabrice Baudoin
Publisher: Springer Nature
ISBN: 3030841413
Category : Mathematics
Languages : en
Pages : 312
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Book Description
This book includes four courses on geometric measure theory, the calculus of variations, partial differential equations, and differential geometry. Authored by leading experts in their fields, the lectures present different approaches to research topics with the common background of a relevant underlying, usually non-Riemannian, geometric structure. In particular, the topics covered concern differentiation and functions of bounded variation in metric spaces, Sobolev spaces, and differential geometry in the so-called Carnot–Carathéodory spaces. The text is based on lectures presented at the 10th School on "Analysis and Geometry in Metric Spaces" held in Levico Terme (TN), Italy, in collaboration with the University of Trento, Fondazione Bruno Kessler and CIME, Italy. The book is addressed to both graduate students and researchers.
Author: George M. Rassias
Publisher: CRC Press
ISBN: 1000950727
Category : Mathematics
Languages : en
Pages : 550
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Book Description
This book contains a series of papers on some of the longstanding research problems of geometry, calculus of variations, and their applications. It is suitable for advanced graduate students, teachers, research mathematicians, and other professionals in mathematics.
Author: Paul Concus
Publisher: Springer Science & Business Media
ISBN: 1461397111
Category : Mathematics
Languages : en
Pages : 213
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Book Description
This volume derives from a workshop on differential geometry, calculus of vari ations, and computer graphics at the Mathematical Sciences Research Institute in Berkeley, May 23-25, 1988. The meeting was structured around principal lectures given by F. Almgren, M. Callahan, J. Ericksen, G. Francis, R. Gulliver, P. Hanra han, J. Kajiya, K. Polthier, J. Sethian, I. Sterling, E. L. Thomas, and T. Vogel. The divergent backgrounds of these and the many other participants, as reflected in their lectures at the meeting and in their papers presented here, testify to the unifying element of the workshop's central theme. Any such meeting is ultimately dependent for its success on the interest and motivation of its participants. In this respect the present gathering was especially fortunate. The depth and range of the new developments presented in the lectures and also in informal discussion point to scientific and technological frontiers be ing crossed with impressive speed. The present volume is offered as a permanent record for those who were present, and also with a view toward making the material available to a wider audience than were able to attend.
Author: Jean-Pierre Bourguignon
Publisher: Springer Nature
ISBN: 303118307X
Category : Mathematics
Languages : en
Pages : 284
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Book Description
This book provides a comprehensive introduction to the Calculus of Variations and its use in modelling mechanics and physics problems. Presenting a geometric approach to the subject, it progressively guides the reader through this very active branch of mathematics, accompanying key statements with a huge variety of exercises, some of them solved. Stressing the need to overcome limitations of the initial point of view, and emphasising the interconnectivity of various branches of mathematics (algebra, analysis and geometry), the book includes some advanced material to challenge the most motivated students. Systematic, short historical notes provide details on the subject’s odyssey, and how new tools have been developed over the last two centuries. This English translation updates a set of notes for a course first given at the École polytechnique in 1987. It will be accessible to graduate students and advanced undergraduates.
Author: Luigi Ambrosio
Publisher: Springer Science & Business Media
ISBN: 3642571867
Category : Mathematics
Languages : en
Pages : 347
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Book Description
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: F. Bethuel
Publisher: Springer
ISBN: 3540488138
Category : Mathematics
Languages : en
Pages : 299
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Book Description
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.
Author: Rupert Frank
Publisher: Springer
ISBN: 9783031676000
Category : Mathematics
Languages : en
Pages : 0
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Book Description
This book is dedicated to exploring optimization problems of geometric-analytic nature, which are fundamental to tackling various unresolved questions in mathematics and physics. These problems revolve around minimizing geometric or analytic quantities, often representing physical energies, within prescribed collections of sets or functions. They serve as catalysts for advancing methodologies in calculus of variations, partial differential equations, and geometric analysis. Furthermore, insights from optimal functional-geometric inequalities enhance analytical problem-solving endeavors. The contributions focus on the intricate interplay between these inequalities and problems of differential and variational nature. Key topics include functional and geometric inequalities, optimal norms, sharp constants in Sobolev-type inequalities, and the regularity of solutions to variational problems. Readers will gain a comprehensive understanding of these concepts, deepening their appreciation for their relevance in mathematical and physical inquiries.
