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Maximum Principles in Differential Equations Murray H. Protter

Maximum Principles in Differential Equations By Murray H. Protter

Maximum Principles in Differential Equations by Murray H. Protter

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Summary

Maximum Principles are central to the theory and applications of second-order partial differential equations and systems. This self-contained text establishes the fundamental principles and provides a variety of applications.

Maximum Principles in Differential Equations Summary

Maximum Principles in Differential Equations by Murray H. Protter

Maximum Principles are central to the theory and applications of second-order partial differential equations and systems. This self-contained text establishes the fundamental principles and provides a variety of applications.

Table of Contents

1. The One-Dimensional Maximum Principle.- 1. The maximum principle.- 2. The generalized maximum principle.- 3. The initial value problem.- 4. Boundary value problems.- 5. Approximation in boundary value problems.- 6. Approximation in the initial value problem.- 7. The eigenvalue problem.- 8. Oscillation and comparison theorems.- 9. Nonlinear operators.- Bibliographical notes.- 2. Elliptic Equations.- 1. The Laplace operator.- 2. Second-order elliptic operators. Transformations.- 3. The maximum principle of E. Hopf.- 4. Uniqueness theorems for boundary value problems.- 5. The generalized maximum principle.- 6. Approximation in boundary value problems.- 7. Green's identities and Green's function.- 8. Eigenvalues.- 9. The Phragmen-Lindeloef principle.- 10. The Harnack inequalities.- 11. Capacity.- 12. The Hadamard three-circles theorem.- 13. Derivatives of harmonic functions.- 14. Boundary estimates for the derivatives.- 15. Applications of bounds for derivatives.- 16. Nonlinear operators.- Bibliographical notes.- 3. Parabolic Equations.- 1. The heat equation.- 2. The one-dimensional parabolic operator.- 3. The general parabolic operator.- 4. Uniqueness theorems for boundary value problems.- 5. A three-curves theorem.- 6. The Phragmen-Lindeloef principle.- 7. Nonlinear operators.- 8. Weakly coupled parabolic systems.- Bibliographical notes.- 4. Hyperbolic Equations.- 1. The wave equation.- 2. The wave operator with lower order terms.- 3. The two-dimensional hyperbolic operator.- 4. Bounds and uniqueness in the initial value problem.- 5. Riemann's function.- 6. Initial-boundary value problems.- 7. Estimates for series solutions.- 8. The two-characteristic problem.- 9. The Goursat problem.- 10. Comparison theorems.- 11. The wave equation in higher dimensions.- Bibliographical notes.

Additional information

NLS9781461297697
9781461297697
1461297699
Maximum Principles in Differential Equations by Murray H. Protter
Murray H. Protter
New
Paperback
Springer-Verlag New York Inc.
2011-09-30
261
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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