Direct Methods in the Calculus of Variations

Name: Direct Methods in the Calculus of Variations
Price: 48.99 USD
Availability: InStock
ISBN: 9789812380432

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 Co Pte Ltd
Binding: Hardcover
Pages: 412
Size: 6.25" wide x 9.00" long x 1.00" tall
Weight: 1.606
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