Partial Differential Equations

Jürgen Jost

326 pages, parution le 18/10/2002

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Résumé

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 one-year course on partial differential equations.
Jürgen Jost is Director 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 Postmodern Analysis (1998), Compact Riemann Surfaces (1997) and Riemannian Geometry and Geometric Analysis (1995). The present book is an expanded translation of the original German version, Partielle Differentialgleichungen (1998).

Contents

Introduction The Laplace equation as the prototype of an elliptic partial differential equation of 2nd order
The maximum principle
Existence techniques I: methods based on the maximum principle
Existence techniques II: Parabolic methods. The Head equation
The wave equation and its connections with the Laplace and heat equation
The heat equation, semigroups, and Brownian motion
The Dirichlet principle. Variational methods for the solution of PDE (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 reqularity theorem of de Giorgi and Nash
Banach and Hilbert spaces. The Lp-spaces
Bibliography.

L'auteur - Jürgen Jost

Honorary Professor, Department of Mathematics, University of Leipzig
Member, Academy of Sciences and Literature, Mainz, the Saxonian Academy of Sciences, Leipzig, and the German Academy of the Natural Scientists - Leopoldina
External Faculty Member, Santa Fe Institute for the Sciences of Complexity, 1399 Hyde Park Road, Santa Fe, NM 87501, USA

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Jürgen Jost
Parution	18/10/2002
Nb. de pages	326
Format	16 x 24
Couverture	Relié
Poids	603g
Intérieur	Noir et Blanc
EAN13	9780387954288
ISBN13	978-0-387-95428-8