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Second Order Partial Differential Equations in Hilbert Spaces

$70.00 ( ) USD

Part of London Mathematical Society Lecture Note Series

  • Date Published: January 2005
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9780511034701

$ 70.00 USD ( )
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About the Authors
  • 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.

    • State of the art treatment of the subject, with numerous references for further reading
    • Inclusion of some essential background helps to make the book self contained
    • Detailed discussion of applications to control theory
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    Reviews & endorsements

    '… 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

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    Product details

    • Date Published: January 2005
    • format: Adobe eBook Reader
    • isbn: 9780511034701
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • 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.

  • Authors

    Giuseppe Da Prato, Scuola Normale Superiore, Pisa

    Jerzy Zabczyk, Polish Academy of Sciences

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