Second order partial differential equations in Hilbert spaces [EBook] / Giuseppe Da Prato, Jerzy Zabczyk.
Second order partial differential equations in Hilbert spaces [EBook] / Giuseppe Da Prato, Jerzy Zabczyk.
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...
Personal Name(s):  Da Prato, Giuseppe, (author) 

Zabczyk, Jerzy, (author)  
Imprint: 
Cambridge :
Cambridge University Press,
2002

Physical Description: 
1 online resource (xvi, 379 pages) 
Note: 
englisch 
ISBN: 
9780511543210 9780521777292 
Series Title: 
London Mathematical Society lecture note series ;
293 
Subject (LOC):  
Full Text 
Table of Contents:
 Theory in Spaces of Continuous Functions
 Gaussian measures
 Introduction and preliminaries
 Definition and first properties of Gaussian measures
 Measures in metric spaces
 Gaussian measures
 Computation of some Gaussian integrals
 The reproducing kernel
 Absolute continuity of Gaussian measures
 Equivalence of product measures in R[superscript [infinity]
 The CameronMartin formula
 The FeldmanHajek theorem
 Brownian motion
 Spaces of continuous functions
 Preliminary results
 Approximation of continuous functions
 Interpolation spaces
 Interpolation between UC[subscript b](H) and UC[superscript 1 subscript b](H)
 Interpolatory estimates
 Additional interpolation results
 The heat equation
 Strict solutions
 Regularity of generalized solutions
 Qderivatives
 Qderivatives of generalized solutions
 Comments on the Gross Laplacian
 The heat semigroup and its generator
 Poisson's equation
 Existence and uniqueness results
 Regularity of solutions
 The equation [Delta subscript Q]u = g
 The Liouville theorem
 Elliptic equations with variable coefficients
 Small perturbations
 Large perturbations
 OrnsteinUhlenbeck equations
 Existence and uniqueness of strict solutions
 Classical solutions
 The OrnsteinUhlenbeck semigroup
 [pi]Convergence
 Properties of the [pi]semigroup (R[subscript t])
 The infinitesimal generator
 Elliptic equations
 Schauder estimates
 The Liouville theorem
 Perturbation results for parabolic equations.