Partial Differential Equations

Jürgen Jost - Collection Graduate Texts in Mathematics

356 pages, parution le 01/02/2007 (2^eme édition)

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Résumé

This book offers an ideal introduction to the theory of partial differential equations. It focuses on elliptic equations and systematically develops the relevant existence schemes, always with a view towards nonlinear problems. It 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. It also explores connections between elliptic, parabolic, and hyperbolic equations as well as the connection with Brownian motion and semigroups. This second edition features a new chapter on reaction-diffusion equations and systems.

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

Sommaire

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
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 L[superscript 2] 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
AppBanach and Hilbert Spaces. The L[superscript P]-Spaces

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Jürgen Jost
Collection	Graduate Texts in Mathematics
Parution	01/02/2007
Édition	2^eme édition
Nb. de pages	356
Format	16 x 23
Couverture	Relié
Poids	635g
Intérieur	Noir et Blanc
EAN13	9780387493183
ISBN13	978-0-387-49318-3