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Lectures in Mathematics. Eth Zürich Ser.: Theorems on Regularity and Singularity of Energy Minimizing Maps by L. Simon (1996, Trade Paperback)
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THEOREMS ON REGULARITY AND SINGULARITY OF ENERGY MINIMIZING MAPS (LECTURES IN MATHEMATICS. ETH ZURICH) By Leon Simon.
- Buy it nowTHEOREMS ON REGULARITY AND SINGULARITY OF ENERGY By Leon Simon
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About this product
Product Identifiers
PublisherSpringer Basel A&G
ISBN-10376435397X
ISBN-139783764353971
eBay Product ID (ePID)9038528053
Product Key Features
Number of PagesVIII, 152 Pages
Publication NameTheorems on Regularity and Singularity of Energy Minimizing Maps
LanguageEnglish
Publication Year1996
SubjectGeometry / Differential, Geometry / Algebraic, Mathematical Analysis
TypeTextbook
AuthorL. Simon
Subject AreaMathematics
SeriesLectures in Mathematics. Eth Zürich Ser.
FormatTrade Paperback
Dimensions
Item Weight23.3 Oz
Item Length10 in
Item Width7 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN96-006193
Dewey Edition20
Number of Volumes1 vol.
IllustratedYes
Dewey Decimal515/.352
Table Of Content1 Analytic Preliminaries.- 1.1 Hölder Continuity.- 1.2 Smoothing.- 1.3 Functions with L2 Gradient.- 1.4 Harmonic Functions.- 1.5 Weakly Harmonic Functions.- 1.6 Harmonic Approximation Lemma.- 1.7 Elliptic regularity.- 1.8 A Technical Regularity Lemma.- 2 Regularity Theory for Harmonic Maps.- 2.1 Definition of Energy Minimizing Maps.- 2.2 The Variational Equations.- 2.3 The ?-Regularity Theorem.- 2.4 The Monotonicity Formula.- 2.5 The Density Function.- 2.6 A Lemma of Luckhaus.- 2.7 Corollaries of Luckhaus' Lemma.- 2.8 Proof of the Reverse Poincaré Inequality.- 2.9 The Compactness Theorem.- 2.10 Corollaries of the ?-Regularity Theorem.- 2.11 Remark on Upper Semicontinuity of the Density ?u(y).- 2.12 Appendix to Chapter 2.- 3 Approximation Properties of the Singular Set.- 3.1 Definition of Tangent Map.- 3.2 Properties of Tangent Maps.- 3.3 Properties of Homogeneous Degree Zero Minimizers.- 3.4 Further Properties of sing u.- 3.5 Definition of Top-dimensional Part of the Singular Set.- 3.6 Homogeneous Degree Zero ? with dim S(?) = n -- 3.- 3.7 The Geometric Picture Near Points of sing*u.- 3.8 Consequences of Uniqueness of Tangent Maps.- 3.9 Approximation properties of subsets of ?n.- 3.10 Uniqueness of Tangent maps with isolated singularities.- 3.11 Functionals on vector bundles.- 3.12 The Liapunov-Schmidt Reduction.- 3.13 The ?ojasiewicz Inequality for ?.- 3.14 ?ojasiewicz for the Energy functional on Sn-1.- 3.15 Proof of Theorem 1 of Section 3.10.- 3.16 Appendix to Chapter 3.- 4 Rectifiability of the Singular Set.- 4.1 Statement of Main Theorems.- 4.2 A general rectifiability lemma.- 4.3 Gap Measures on Subsets of ?n.- 4.4 Energy Estimates.- 4.5 L2 estimates.- 4.6 The deviation function ?.- 4.7 Proof of Theorems 1, 2 of Section 4.1.- 4.8 The case when ?has arbitrary Riemannian metric.
SynopsisThe aim of these lecture notes is to give an essentially self-contained introduction to the basic regularity theory for energy minimizing maps, including recent developments concerning the structure of the singular set and asymptotics on approach to the singular set. Specialized knowledge in partial differential equations or the geometric calculus of variations is not required; a good general background in mathematical analysis would be adequate preparation.
LC Classification NumberQA614-614.97
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