Lectures on Geometric Measure Theory
Author : Leon Simon
Publisher :
Page : 286 pages
File Size : 46,38 MB
Release : 1984
Category : Geometric measure theory
ISBN : 9780867844290
Author : Leon Simon
Publisher :
Page : 286 pages
File Size : 46,38 MB
Release : 1984
Category : Geometric measure theory
ISBN : 9780867844290
Author : Leon Simon
Publisher :
Page : pages
File Size : 38,7 MB
Release : 1980
Category :
ISBN :
Author : Guido De Philippis
Publisher : Springer Nature
Page : 138 pages
File Size : 45,97 MB
Release : 2021-03-23
Category : Mathematics
ISBN : 303065799X
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.
Author : Herbert Federer
Publisher : Springer
Page : 694 pages
File Size : 24,68 MB
Release : 2014-11-25
Category : Mathematics
ISBN : 3642620108
"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)
Author : Alessio Figalli
Publisher : Springer
Page : 224 pages
File Size : 16,64 MB
Release : 2018-05-23
Category : Mathematics
ISBN : 3319740423
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.
Author : E. Bombieri
Publisher : Springer Science & Business Media
Page : 227 pages
File Size : 22,60 MB
Release : 2011-06-04
Category : Mathematics
ISBN : 3642109705
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.
Author : Steven G. Krantz
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 44,57 MB
Release : 2008-12-15
Category : Mathematics
ISBN : 0817646795
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.
Author : William K. Allard
Publisher : American Mathematical Soc.
Page : 482 pages
File Size : 33,62 MB
Release : 1986
Category : Mathematics
ISBN : 0821814702
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 : Camillo De Lellis
Publisher : European Mathematical Society
Page : 140 pages
File Size : 16,37 MB
Release : 2008
Category : Mathematics
ISBN : 9783037190449
The characterization of rectifiable sets through the existence of densities is a pearl of geometric measure theory. The difficult proof, due to Preiss, relies on many beautiful and deep ideas and novel techniques. Some of them have already proven useful in other contexts, whereas others have not yet been exploited. These notes give a simple and short presentation of the former and provide some perspective of the latter. This text emerged from a course on rectifiability given at the University of Zurich. It is addressed both to researchers and students; the only prerequisite is a solid knowledge in standard measure theory. The first four chapters give an introduction to rectifiable sets and measures in Euclidean spaces, covering classical topics such as the area formula, the theorem of Marstrand and the most elementary rectifiability criterions. The fifth chapter is dedicated to a subtle rectifiability criterion due to Marstrand and generalized by Mattila, and the last three focus on Preiss' result. The aim is to provide a self-contained reference for anyone interested in an overview of this fascinating topic.
Author : Harold Widom
Publisher : Courier Dover Publications
Page : 177 pages
File Size : 14,99 MB
Release : 2016-11-16
Category : Mathematics
ISBN : 0486810283
These well-known and concise lecture notes present the fundamentals of the Lebesgue theory of integration and an introduction to some of the theory's applications. Suitable for advanced undergraduates and graduate students of mathematics, the treatment also covers topics of interest to practicing analysts. Author Harold Widom emphasizes the construction and properties of measures in general and Lebesgue measure in particular as well as the definition of the integral and its main properties. The notes contain chapters on the Lebesgue spaces and their duals, differentiation of measures in Euclidean space, and the application of integration theory to Fourier series.