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, 2007.
• Έκδοση: Second Edition.
• Σειρά: Graduate Texts in Mathematics, 214
• Θέματα: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Partial differential equations.; Physics.; Analysis.; Theoretical, Mathematical and Computational Physics.; Partial Differential Equations.; Numerical and Computational Physics.

This book is intended for students who wish to get an introduction to the theory of partial differential equations. The author focuses on elliptic equations and systematically develops the relevant existence schemes, always with a view towards nonlinear problems. These are maximum principle methods...

Πίνακας περιεχομένων:

• Introduction: What Are Partial Differential Equations?
• The Laplace Equation as the Prototype of an Elliptic Partial Differential Equation of Second Order
• The Maximum Principle
• Existence Techniques I: Methods Based on the Maximum Principle
• Existence Techniques II: Parabolic Methods. The Heat Equation
• Reaction-Diffusion Equations and Systems
• The Wave Equation and its Connections with the Laplace and Heat Equations
• The Heat Equation, Semigroups, and Brownian Motion
• The Dirichlet Principle. Variational Methods for the Solution of PDEs (Existence Techniques III)
• Sobolev Spaces and L2 Regularity Theory
• Strong Solutions
• The Regularity Theory of Schauder and the Continuity Method (Existence Techniques IV)
• The Moser Iteration Method and the Regularity Theorem of de Giorgi and Nash.