Partial Differential Equations

• Κύριος συγγραφέας: Jost, Jürgen (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: New York, NY : Springer New York : Imprint: Springer, 2013.
• Έκδοση: 3rd ed. 2013.
• Σειρά: Graduate Texts in Mathematics, 214
• Θέματα: Mathematics.; Partial differential equations.; Physics.; Partial Differential Equations.; Theoretical, Mathematical and Computational Physics.

This book offers an ideal graduate-level introduction to the theory of partial differential equations.  The first part of the book describes the basic mathematical problems and structures associated with elliptic, parabolic, and hyperbolic partial differential equations, and explores the connections...

Πίνακας περιεχομένων:

• Preface
• Introduction: What are Partial Differential Equations?
• 1 The Laplace equation as the Prototype of an Elliptic Partial Differential Equation of Second Order
• 2 The Maximum Principle
• 3 Existence Techniques I: Methods Based on the Maximum Principle
• 4 Existence Techniques II: Parabolic Methods. The Heat Equation
• 5 Reaction-Diffusion Equations and Systems
• 6 Hyperbolic Equations
• 7 The Heat Equation, Semigroups, and Brownian Motion.- 8 Relationships between Different Partial Differential Equations
• 9 The Dirichlet Principle. Variational Methods for the Solutions of PDEs (Existence Techniques III)
• 10 Sobolev Spaces and L^2 Regularity theory
• 11 Strong solutions
• 12 The Regularity Theory of Schauder and the Continuity Method (Existence Techniques IV)
• 13The Moser Iteration Method and the Regularity Theorem of de Giorgi and Nash
• Appendix: Banach and Hilbert spaces. The L^p-Spaces
• References
• Index of Notation
• Index.