Second order partial differential equations in Hilbert spaces [E-Book] / Giuseppe Da Prato, Jerzy Zabczyk.
Da Prato, Giuseppe, (author)
Zabczyk, Jerzy, (author)
Cambridge : Cambridge University Press, 2002
1 online resource (xvi, 379 pages)
englisch
9780511543210
9780521777292
London Mathematical Society lecture note series ; 293
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 Cameron-Martin formula
  • The Feldman-Hajek 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
  • Q-derivatives
  • Q-derivatives 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
  • Ornstein-Uhlenbeck equations
  • Existence and uniqueness of strict solutions
  • Classical solutions
  • The Ornstein-Uhlenbeck 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.