Direct Methods in the Calculus of Variations

ISBN-10: 9812380434

ISBN-13: 9789812380432

Edition: 2003

Authors: Enrico Giusti
List price: $96.00
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Book details

List price: $96.00
Copyright year: 2003
Publisher: World Scientific Publishing Company, Incorporated
Binding: Hardcover
Pages: 412
Size: 6.25" wide x 9.00" long x 1.00" tall
Weight: 1.584
Language: English

Introduction
Semi-Classical Theory
The Maximum Principle
The Bounded Slope Condition
Barriers
The Area Functional
Non-Existence of Minimal Surfaces
Measurable Functions
L[superscript p] Spaces
Test Functions and Mollifiers
Morrey's and Campanato's Spaces
The Lemmas of John and Nirenberg
Interpolation
The Hausdorff Measure
Sobolev Spaces
Partitions of Unity
Weak Derivatives
The Sobolev Spaces W[superscript k,p]
Imbedding Theorems
Compactness
Inequalities
Traces
The Values of W[superscript 1,p] Functions
Convexity and Semicontinuity
Preliminaries
Convex Functionals
Semicontinuity
An Existence Theorem
Quasi-Convex Functionals
Necessary Conditions
First Semicontinuity Results
The Quasi-Convex Envelope
The Ekeland Variational Principle
Semicontinuity
Coerciveness and Existence
Quasi-Minima
Preliminaries
Quasi-Minima and Differential Quations
Cubical Quasi-Minima
L[superscript p] Estimates for the Gradient
Boundary Estimates
Holder Continuity
Caccioppoli's Inequality
De Giorgi Classes
Quasi-Minima
Boundary Regularity
The Harnack Inequality
The Homogeneous Case
[omega]-Minima
Boundary Regularity
First Derivatives
The Difference Quotients
Second Derivatives
Gradient Estimates
Boundary Estimates
[omega]-Minima
Holder Continuity of the Derivatives (p = 2)
Other Gradient Estimates
Holder Continuity of the Derivatives p [is not equal to] 2
Elliptic Equations
Partial Regularity
Preliminaries
Quadratic Functionals
The Second Caccioppoli Inequality
The Case F = F(z) (p = 2)
Partial Regularity
Higher Derivatives
Hilbert Regularity
Constant Coefficients
Continuous Coefficients
L[superscript p] Estimates
Minima of Functionals
References
Index
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