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AuthorProtter, Murray H. author
TitleMaximum Principles in Differential Equations [electronic resource] / by Murray H. Protter, Hans F. Weinberger
ImprintNew York, NY : Springer New York, 1984
Connect tohttp://dx.doi.org/10.1007/978-1-4612-5282-5
Descript X, 261 p. online resource

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


CONTENT

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. Greenโ{128}{153}s identities and Greenโ{128}{153}s function -- 8. Eigenvalues -- 9. The Phragmรจn-Lindelรถf 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 Phragmรจn-Lindelรถf 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. Riemannโ{128}{153}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


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