Sets of finite perimeter and geometric variational problems : an introduction to geometric measure theory / Francesco Maggi

Auteur principal : Maggi, Francesco, 1978-, AuteurType de document : MonographieCollection : Cambridge studies in advanced mathematics, 135Langue : anglais.Pays: Grande Bretagne.Éditeur : Cambridge : Cambridge University Press, cop. 2012Description : 1 vol. (XIX-454 p.) : fig. ; 24 cmISBN: 9781107021037.ISSN: 0950-6330.Bibliographie : Bibliogr. p. 445-452. Index.Sujet MSC : 49Q15, Calculus of variations and optimal control; optimization - Manifolds and measure-geometric topics, Geometric measure and integration theory, integral and normal currents in optimization
49-01, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to calculus of variations and optimal control
26B20, Real functions - Functions of several variables, Integral formulas (Stokes, Gauss, Green, etc.)
49Q05, Calculus of variations and optimal control; optimization - Manifolds and measure-geometric topics, Minimal surfaces and optimization
28A75, Classical measure theory, Length, area, volume, other geometric measure theoryEn-ligne : zbMath | MSN | CUP
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Item type Current library Call number Status Date due Barcode
Monographie Monographie CMI
Salle 1 		49 MAG (Browse shelf(Opens below)) Available 12577-01

This book originates from the lecture notes that the author held at the University of Duisburg-Essen in 2005. The first aim of the book was to provide an introduction for the beginners about theory of sets of finite perimeter, presenting some results concerning the existence, symmetry, regularity and structure of singularities in some variational problems involving the length and area. Topics like the Euclidean isoperimetric problem, the description of geometric properties of equilibrium shapes for liquid drops and crystals, the regularity up to a singular set of codimension at least 8 for area minimizing boundaries, and the theory of minimizing clusters are covered. The secondary aim of this book is to provide a multi-leveled introduction to the study of other variational problems (parametric and non-parametric) as well as of partial differential equations. In this way, an interested reader is able to enter with relative ease several parts of Geometric Measure Theory and to apply some tools from this theory in the study of other problems from Mathematics ... (zbMath)

Bibliogr. p. 445-452. Index

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