Lecture Notes in Mathematics

Uniqueness and Non-Uniqueness of Semigroups Generated by Singular Diffusion Operators

Authors: Eberle, Andreas

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About this book

This book addresses both probabilists working on diffusion processes and analysts interested in linear parabolic partial differential equations with singular coefficients. The central question discussed is whether a given diffusion operator, i.e., a second order linear differential operator without zeroth order term, which is a priori defined on test functions over some (finite or infinite dimensional) state space only, uniquely determines a strongly continuous semigroup on a corresponding weighted Lp space. Particular emphasis is placed on phenomena causing non-uniqueness, as well as on the relation between different notions of uniqueness appearing in analytic and probabilistic contexts.

Table of contents (6 chapters)

  • Introduction

    Eberle, Andreas

    Pages 1-8

  • Motivation and basic definitions: Uniqueness problems in various contexts

    Eberle, Andreas

    Pages 9-40

  • L p uniqueness in finite dimensions

    Eberle, Andreas

    Pages 41-87

  • Markov uniqueness

    Eberle, Andreas

    Pages 89-167

  • Probabilistic aspects of L p and Markov uniqueness

    Eberle, Andreas

    Pages 169-184

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-540-48076-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.95
price for USA
  • ISBN 978-3-540-66628-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Uniqueness and Non-Uniqueness of Semigroups Generated by Singular Diffusion Operators
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1718
Copyright
1999
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-48076-1
DOI
10.1007/BFb0103045
Softcover ISBN
978-3-540-66628-8
Series ISSN
0075-8434
Edition Number
1
Number of Pages
VIII, 268
Topics