Avner Friedman

Partial Differential Equations

• Broschiertes Buch

Produktbeschreibung

Largely self-contained, this three-part treatment focuses on elliptic and evolution equations, concluding with a series of independent topics directly related to the methods and results of the preceding sections. 1969 edition.

---

Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.

Produktdetails

• Verlag: Dover Publications
• Seitenzahl: 272
• Erscheinungstermin: 24. November 2008
• Englisch
• Abmessung: 229mm x 152mm x 15mm
• Gewicht: 340g
• ISBN-13: 9780486469195
• ISBN-10: 0486469190
• Artikelnr.: 24628951

Autorenporträt

Avner Friedman taught mathematics at Indiana University, the University of California at Berkeley, the University of Minnesota, Stanford, and Northwestern University. He received Sloan and Guggenheim Fellowships and is the author of six other Dover books.

Inhaltsangabe

Part 1. Elliptic Equations 1. Definitions 2. Green's Identity 3.
Fundamental Solutions 4. Construction of Fundamental Solutions 5. Partition
of Unity 6. Weak and Strong Derivatives 7. Strong Derivative as a Local
Property 8. Calculus Inequalities 9. Extended Sobolev Inequalities in
R(superscript n) 10. Extended Sobolev Inequalities in Bounded Domains 11.
Imbedding Theorems 12. Gärding's Inequality 13. The Dirichlet Problem 14.
Existence Theory 15-16. Regularity in the Interior 17. Regularity on the
Boundary 18. A Priori Inequalities 19. General Boundary Conditions 20.
Problems Part 2. Evolution Equations 1. Strongly Continuous Semigroups 2.
Analytic Semigroups 3. Fundamental Solutions and the Cauchy Problems 4-5.
Construction of Fundamental Solutions 6. Uniqueness of Fundamental
Solutions 7. Solution of the Cauchy Problem 8. Differentiability of
Solutions 9. The Initial-Boundary Value Problem for Parabolic Equations 10.
Smoothness of the Solutions of the Initial-Boundary Value Problem 11. A
Differentiability Theorem in Hilbert Space 12. A Uniqueness Theorem in
Hilbert Space 13. Convergence of Solutions as t --> infinity 14. Fractional
Powers of Operators 15. Proof of Lemma 14.5 16. Nonlinear Evolution
Equations 17. Nonlinear Parabolic Equations 18. Uniqueness for Backward
Equations 19. Lower Bounds on Solutions as t --> infinity 20. Problems Part
3. Selected Topics 1. Analyticity of Solutions of Elliptic Equations 2.
Analyticity of Solutions of Evolution Equations 3. Analyticity of Solutions
of Parabolic Equations 4. Lower Bounds for Solutions of Evolution
Inequalities 5. Weighted Elliptic Equations 6. Asymptotic Expansions of
Solutions of Evolution Equations 7. Asymptotic Behavior of Solutions of
Elliptic Equations 8. Integral Equations in Banach Space 9. Optimal Control
in Banach Space Bibliographical Remarks Bibliography