Second Order Partial Differential Equations in Hilbert Spaces

by Giuseppe Da Prato, Jerzy Zabczyk

Overview

Second order linear parabolic and elliptic equations arise frequently in mathematical physics, biology and finance. Here the authors present a state of the art treatment of the subject from a new perspective. They then go on to discuss how the results in the book can be applied to control theory. This area is developing rapidly and there are numerous notes and references that point the reader to more specialized results not covered in the book. Coverage of some essential background material helps to make the book self contained.

Product Details

ISBN-13:	9780521777292
Publisher:	Cambridge University Press
Publication date:	07/25/2002
Series:	London Mathematical Society Lecture Note Series , #293
Pages:	396
Product dimensions:	5.98(w) x 9.02(h) x 0.87(d)

Table of Contents

Part I. Theory in the Space of Continuous Functions: 1. Gaussian measures; 2. Spaces of continuous functions; 3. 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; Part II. Theory in Sobolev Spaces with a Gaussian Measure: 9. L2 and Sobolev spaces; 10. Ornstein-Uhlenbeck semigroups on Lp(H, mu); 11. Perturbations of Ornstein-Uhlenbeck semigroups; 12. Gradient systems; Part II. Applications to Control Theory: 13. Second order Hamilton-Jacobi equations; 14. Hamilton-Jacobi inclusions.

Editorial Reviews

'… can be warmly recommended to anyone interested in the field.' European Mathematical Society Newsletter

'… the authors five an almost optimal presentation: making the central ideas clear, not hiding the problems and the technical efforts needed to overcome them, and discussing in an appropriate way relations to existing work. … it will be of enormous help to experts of PhD students starting to work in the field. The LMS Lecture Note Series has the aim of providing 'volumes [that] are short monographs giving authoritative accounts of the present state of knowledge on a topic of general interest'. The authors have done a fine job, and have successfully achieved this goal.' Niels Jacob, University of Wales, Swansea

From the Publisher

Da Prato (Scuola Normale Superiore di Pisa) and Zabczyk (Polish Academy of Sciences, Warsaw) present the state of the rapidly evolving art of the theory of parabolic/elliptic equations in an infinite dimensional Hilbert space—theory relevant to functional analysis, mathematical physics, and applied mathematics. The theoretical section covers spaces of continuous functions and Sobolev spaces. Applications to control theory are then discussed. Appendices address interpolation spaces, null controllability, and semiconcave functions and Hamilton-Jacobi semigroups. Annotation c. Book News, Inc., Portland, OR