Author | Eberle, Andreas. author |
---|---|

Title | Uniqueness and Non-Uniqueness of Semigroups Generated by Singular Diffusion Operators [electronic resource] / by Andreas Eberle |

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1999 |

Connect to | http://dx.doi.org/10.1007/BFb0103045 |

Descript | VIII, 268 p. online resource |

SUMMARY

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

CONTENT

Motivation and basic definitions: Uniqueness problems in various contexts -- L p uniqueness in finite dimensions -- Markov uniqueness -- Probabilistic aspects of L p and Markov uniqueness -- First steps in infinite dimensions

Mathematics
Group theory
Partial differential equations
Potential theory (Mathematics)
Probabilities
Mathematics
Probability Theory and Stochastic Processes
Partial Differential Equations
Group Theory and Generalizations
Potential Theory