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

  • Authors
  • AndreasĀ Eberle
Part of the Lecture Notes in Mathematics book series (LNM, volume 1718)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Andreas Eberle
    Pages 1-8
  3. Andreas Eberle
    Pages 41-87
  4. Andreas Eberle
    Pages 89-167
  5. Andreas Eberle
    Pages 185-253
  6. Back Matter
    Pages 255-260

About this book

Introduction

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.

Keywords

Differential operator differential equation diffusion process essentially self-adjoint generator partial differential equation semigroup uniqueness

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0103045
  • Copyright Information Springer-Verlag Berlin Heidelberg 1999
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-66628-8
  • Online ISBN 978-3-540-48076-1
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692