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Elliptic partial differential equations of second order

Author: David Gilbarg; Neil S Trudinger
Publisher: Berlin : Springer, 2001.
Series: Classics in mathematics.
Edition/Format:   Print book : English : Reprint of the 1998 edView all editions and formats
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From the reviews: "This is a book of interest to any having to work with differential equations, either as a reference or as a book to learn from. The authors have taken trouble to make the treatment  Read more...

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Document Type: Book
All Authors / Contributors: David Gilbarg; Neil S Trudinger
ISBN: 3540411607 9783540411604
OCLC Number: 639237067
Description: XIII, 517 p. ; 24 cm.
Contents: Chapter 1. Introduction Part I: Linear EquationsChapter 2. Laplace's Equation2.1 The Mean Value Inequalities2.2 Maximum and Minimum Principle2.3 The Harnack Inequality2.4 Green's Representation2.5 The Poisson Integral2.6 Convergence Theorems2.7 Interior Estimates of Derivatives2.8 The Dirichlet Problem; the Method of Subharmonic Functions2.9 CapacityProblemsChapter 3. The Classical Maximum Principle3.1 The Weak Maximum Principle3.2 The Strong Maximum Principle3.3 Apriori Bounds3.4 Gradient Estimates for Poisson's Equation3.5 A Harnack Inequality3.6 Operators in Divergence FormNotesProblemsChapter 4. Poisson's Equation and Newtonian Potential4.1 Hoelder Continuity4.2 The Dirichlet Problem for Poisson's Equation4.3 Hoelder Estimates for the Second Derivatives4.4 Estimates at the Boundary4.5 Hoelder Estimates for the First DerivativesNotes ProblemsChapter 5. Banach and Hilbert Spaces5.1 The Contraction Mapping5.2 The Method of Cintinuity5.3 The Fredholm Alternative5.4 Dual Spaces and Adjoints5.5 Hilbert Spaces5.6 The Projection Theorem5.7 The Riesz Representation Theorem5.8 The Lax-Milgram Theorem5.9 The Fredholm Alternative in Hilbert Spaces5.10 Weak CompactnessNotesProblemsChapter 6. Classical Solutions; the Schauder Approach6.1 The Schauder Interior Estimates6.2 Boundary and Global Estimates6.3 The Dirichlet Problem6.4 Interior and Boundary Regularity6.5 An Alternative Approach6.6 Non-Uniformly Elliptic Equations6.7 Other Boundary Conditions; the Obliue Derivative Problem 6.8 Appendix 1: Interpolation Inequalities6.9 Appendix 2: Extension LemmasNotesProblemsChapter 7. Sobolev Spaces7.1 L^p spaces7.2 Regularization and Approximation by Smooth Functions7.3 Weak Derivatives7.4 The Chain Rule7.5 The W^(k,p) Spaces7.6 DensityTheorems7.7 Imbedding Theorems7.8 Potential Estimates and Imbedding Theorems7.9 The Morrey and John-Nirenberg Estimes7.10 Compactness Results7.11 Difference Quotients7.12 Extension and InterpolationNotesProblemsChapter 8 Generalized Solutions and Regularity8.1 The Weak Maximum Principle8.2 Solvability of the Dirichlet Problem8.3 Diferentiability of Weak Solutions8.4 Global Regularity8.5 Global Boundedness of Weak Solutions8.6 Local Properties of Weak Solutions8.7 The Strong Maximum Principle8.8 The Harnack Inequality8.9 Hoelder Continuity8.10 Local Estimates at the Boundary8.11 Hoelder Estimates for the First Derivatives8.12 The Eigenvalue ProblemNotesProblemsChapter 9. Strong Solutions9.1 Maximum Princiles for Strong Solutions9.2 L^p Estimates: Preliminary Analysis9.3 The Marcinkiewicz Interpolation Theorem9.4 The Calderon-Zygmund Inequality9.5 L^p Estimates9.6 The Dirichlet Problem9.7 A Local Maximum Principle9.8 Hoelder and Harnack Estimates9.9 Local Estimates at the BoundaryNotesProblemsPart II: Quasilinear EquationsChapter 10. Maximum and Comparison Principles 10.1 The Comparison Principle 10.2 Maximum Principles 10.3 A Counterexample 10.4 Comparison Principles for Divergence Form Operators 10.5 Maximum Principles for Divergence Form Operators Notes ProblemsChapter 11. Topological Fixed Point Theorems and Their Application11.1 The Schauder Fixes Point Theorem11.2 The Leray-Schauder Theorem: a Special Case11.3 An Application11.4 The Leray-Schauder Fixed Point Theorem11.5 Variational ProblemsNotesChapter 12. Equations in Two Variables12.1 Quasiconformal Mappings12.2 hoelder Gradient Estimates for Linear Equations12.3 The Dirichlet Problem for Uniformly Elliptic Equations12.4 Non-Uniformly Elliptic EquationsNotesProblemsChapter 13. Hoelder Estimates for
Series Title: Classics in mathematics.
Responsibility: David Gilbarg, Neil S. Trudinger.

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From the reviews:"The aim of the book is to present "the systematic development of the general theory of second order quasilinear elliptic equations and of the linear theory required in the process". Read more...

 
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