Second Order Partial Differential Equations in Hilbert Spaces

Giuseppe Da Prato, Jerzy Zabczyk

380 pages, parution le 04/11/2002

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Résumé

Second order linear parabolic and elliptic equations arise frequently in mathematics and other disciplines. For example parabolic equations are to be found in statistical mechanics and solid state theory, their infinite dimensional counterparts are important in fluid mechanics, mathematical finance and population biology, whereas nonlinear parabolic equations arise in control theory. Here the authors present a state of the art treatment of the subject from a new perspective. The main tools used are probability measures in Hilbert and Banach spaces and stochastic evolution equations. There is then a discussion of how the results in the book can be applied to control theory. This area is developing very rapidly and there are numerous notes and references that point the reader to more specialised results not covered in the book. Coverage of some essential background material will help make the book self-contained and increase its appeal to those entering the subject.

Contents
I Theory in Spaces of Continuous Functions

1 Gaussian measures
2 Spaces of continuous functions
3 The heat equation
4 Poisson's equation
5 Elliptic equations with variable coefficients
6 Ornstein-Uhlenbeck equations
7 General parabolic equations
8 Parabolic equations in open sets

II Theory in Sobolev Spaces

9 L²and Sobolev spaces
10 Ornstein-Uhlenbeck semigroups on L^p (H,μ)
11 Perturbations of Ornstein-Uhlenbeck semigroups
12 Gradient systems

III Applications to Control Theory

13 Second order Hamilton-Jacobi equations
14 Hamilton-Jacobi inclusions

IV Appendices

A Interpolation spaces
B Null controllability
C Semiconcave functions and Hamilton-Jacobi semigroups
Bibliography
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Giuseppe Da Prato, Jerzy Zabczyk
Parution	04/11/2002
Nb. de pages	380
Format	15 x 22,5
Couverture	Broché
Poids	540g
Intérieur	Noir et Blanc
EAN13	9780521777292
ISBN13	978-0-521-77729-2