Partial Differential Equations [electronic resource] / by Jürgen Jost.
By: Jost, Jürgen [author.].
Contributor(s): SpringerLink (Online service).
Material type: TextSeries: Graduate Texts in Mathematics: 214Publisher: New York, NY : Springer New York, 2007Edition: Second Edition.Description: XIV, 356 p. 10 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9780387493190.Subject(s): Global analysis (Mathematics)  Differential equations, partial  Analysis  Theoretical, Mathematical and Computational Physics  Partial Differential Equations  Numerical and Computational Physics, SimulationAdditional physical formats: Printed edition:: No title; Printed edition:: No title; Printed edition:: No titleDDC classification: 515 Online resources: Click here to access onlineItem type  Current location  Call number  Status  Date due  Barcode  Item holds  

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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  ReactionDiffusion 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.
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 (particularly important for numerical analysis schemes), parabolic equations, variational methods, and continuity methods. This book also develops the main methods for obtaining estimates for solutions of elliptic equations: Sobolev space theory, weak and strong solutions, Schauder estimates, and Moser iteration. Connections between elliptic, parabolic, and hyperbolic equations are explored, as well as the connection with Brownian motion and semigroups. This book can be utilized for a oneyear course on partial differential equations. For the new edition the author has added a new chapter on reactiondiffusion equations and systems. There is also new material on Neumann boundary value problems, Poincaré inequalities, expansions, as well as a new proof of the Hölder regularity of solutions of the Poisson equation. Jürgen Jost is CoDirector of the Max Planck Institute for Mathematics in the Sciences and Professor of Mathematics at the University of Leipzig. He is the author of a number of Springer books, including Dynamical Systems (2005), Postmodern Analysis (3rd ed. 2005, also translated into Japanese), Compact Riemann Surfaces (3rd ed. 2006) and Riemannian Geometry and Geometric Analysis (4th ed., 2005). The present book is an expanded translation of the original German version, Partielle Differentialgleichungen (1998). About the first edition: Because of the nice global presentation, I recommend this book to students and young researchers who need the now classical properties of these secondorder partial differential equations. Teachers will also find in this textbook the basis of an introductory course on secondorder partial differential equations.  Alain Brillard, Mathematical Reviews Beautifully written and superbly wellorganised, I strongly recommend this book to anyone seeking a stylish, balanced, uptodate survey of this central area of mathematics.  Nick Lord, The Mathematical Gazette.
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Partial differential equations by Jost Jurgen 
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