Geometric Measure Theory And The Calculus Of Variations
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Geometric Measure Theory And The Calculus Of Variations
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Author : William K. Allard
language : en
Publisher: American Mathematical Soc.
Release Date : 1986
Geometric Measure Theory And The Calculus Of Variations written by William K. Allard and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
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.
Geometric Measure Theory
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Author : Frank Morgan
language : en
Publisher: Academic Press
Release Date : 2016-05-02
Geometric Measure Theory written by Frank Morgan and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-02 with Mathematics categories.
Geometric Measure Theory: A Beginner's Guide, Fifth Edition provides the framework readers need to understand the structure of a crystal, a soap bubble cluster, or a universe. The book is essential to any student who wants to learn geometric measure theory, and will appeal to researchers and mathematicians working in the field. Brevity, clarity, and scope make this classic book an excellent introduction to more complex ideas from geometric measure theory and the calculus of variations for beginning graduate students and researchers. Morgan emphasizes geometry over proofs and technicalities, providing a fast and efficient insight into many aspects of the subject, with new coverage to this edition including topical coverage of the Log Convex Density Conjecture, a major new theorem at the center of an area of mathematics that has exploded since its appearance in Perelman's proof of the Poincaré conjecture, and new topical coverage of manifolds taking into account all recent research advances in theory and applications. Focuses on core geometry rather than proofs, paving the way to fast and efficient insight into an extremely complex topic in geometric structures Enables further study of more advanced topics and texts Demonstrates in the simplest possible way how to relate concepts of geometric analysis by way of algebraic or topological techniques Contains full topical coverage of The Log-Convex Density Conjecture Comprehensively updated throughout
Geometric Measure Theory
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Author : Herbert Federer
language : en
Publisher: Springer
Release Date : 2014-11-25
Geometric Measure Theory written by Herbert Federer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-25 with Mathematics categories.
"This book is a major treatise in mathematics and is essential in the working library of the modern analyst." (Bulletin of the London Mathematical Society)
Partial Differential Equations And Geometric Measure Theory
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Author : Alessio Figalli
language : en
Publisher: Springer
Release Date : 2018-05-23
Partial Differential Equations And Geometric Measure Theory written by Alessio Figalli and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-23 with Mathematics categories.
This book collects together lectures by some of the leaders in the field of partial differential equations and geometric measure theory. It features a wide variety of research topics in which a crucial role is played by the interaction of fine analytic techniques and deep geometric observations, combining the intuitive and geometric aspects of mathematics with analytical ideas and variational methods. The problems addressed are challenging and complex, and often require the use of several refined techniques to overcome the major difficulties encountered. The lectures, given during the course "Partial Differential Equations and Geometric Measure Theory'' in Cetraro, June 2–7, 2014, should help to encourage further research in the area. The enthusiasm of the speakers and the participants of this CIME course is reflected in the text.
Geometric Measure Theory
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Author : Fanghua Lin
language : en
Publisher:
Release Date : 2002
Geometric Measure Theory written by Fanghua Lin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Geometric measure theory categories.
This work is intended to give a quick overview on the subject of the geometric measure theory with emphases on various basic ideas, techniques and their applications in problems arising in the calculus of variations, geometrical analysis and nonlinear partial differential equations.
New Trends On Analysis And Geometry In Metric Spaces
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Author : Fabrice Baudoin
language : en
Publisher: Springer Nature
Release Date : 2022-02-04
New Trends On Analysis And Geometry In Metric Spaces written by Fabrice Baudoin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-04 with Mathematics categories.
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.
Topics In The Calculus Of Variations
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Author : Martin Fuchs
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Topics In The Calculus Of Variations written by Martin Fuchs and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
This book illustrates two basic principles in the calculus of variations which are the question of existence of solutions and closely related the problem of regularity of minimizers. Chapter one studies variational problems for nonquadratic energy functionals defined on suitable classes of vectorvalued functions where also nonlinear constraints are incorporated. Problems of this type arise for mappings between Riemannian manifolds or in nonlinear elasticity. Using direct methods the existence of generalized minimizers is rather easy to establish and it is then shown that regularity holds up to a set of small measure. Chapter two contains a short introduction into Geometric Measure Theory which serves as a basis for developing an existence theory for (generalized) manifolds with prescribed mean curvature form and boundary in arbitrary dimensions and codimensions. One major aspect of the book is to concentrate on techniques and to present methods which turn out to be useful for applications in regularity theorems as well as for existence problems.
Geometric Measure Theory And Minimal Surfaces
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Author : E. Bombieri
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-04
Geometric Measure Theory And Minimal Surfaces written by E. Bombieri and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-04 with Mathematics categories.
W.K. ALLARD: On the first variation of area and generalized mean curvature.- F.J. ALMGREN Jr.: Geometric measure theory and elliptic variational problems.- E. GIUSTI: Minimal surfaces with obstacles.- J. GUCKENHEIMER: Singularities in soap-bubble-like and soap-film-like surfaces.- D. KINDERLEHRER: The analyticity of the coincidence set in variational inequalities.- M. MIRANDA: Boundaries of Caciopoli sets in the calculus of variations.- L. PICCININI: De Giorgi’s measure and thin obstacles.
Geometric Measure Theory And Free Boundary Problems
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Author : Guido De Philippis
language : en
Publisher: Springer Nature
Release Date : 2021-03-23
Geometric Measure Theory And Free Boundary Problems written by Guido De Philippis and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-23 with Mathematics categories.
This volume covers contemporary aspects of geometric measure theory with a focus on applications to partial differential equations, free boundary problems and water waves. It is based on lectures given at the 2019 CIME summer school “Geometric Measure Theory and Applications – From Geometric Analysis to Free Boundary Problems” which took place in Cetraro, Italy, under the scientific direction of Matteo Focardi and Emanuele Spadaro. Providing a description of the structure of measures satisfying certain differential constraints, and covering regularity theory for Bernoulli type free boundary problems and water waves as well as regularity theory for the obstacle problems and the developments leading to applications to the Stefan problem, this volume will be of interest to students and researchers in mathematical analysis and its applications.
Geometric Integration Theory
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Author : Steven G. Krantz
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-15
Geometric Integration Theory written by Steven G. Krantz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-15 with Mathematics categories.
This textbook introduces geometric measure theory through the notion of currents. Currents, continuous linear functionals on spaces of differential forms, are a natural language in which to formulate types of extremal problems arising in geometry, and can be used to study generalized versions of the Plateau problem and related questions in geometric analysis. Motivating key ideas with examples and figures, this book is a comprehensive introduction ideal for both self-study and for use in the classroom. The exposition demands minimal background, is self-contained and accessible, and thus is ideal for both graduate students and researchers.