Uniqueness and Non-Uniqueness of Semigroups Generated by Singular Diffusion Operators / by Andreas Eberle.

Format:

Book

Author/Creator:

Eberle, Andreas, 1969- author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1718.

Lecture Notes in Mathematics, 0075-8434 ; 1718

Language:

English

Subjects (All):

Distribution (Probability theory).

Differential equations, Partial.

Group theory.

Potential theory (Mathematics).

Probability Theory and Stochastic Processes.

Partial Differential Equations.

Group Theory and Generalizations.

Potential Theory.

Local Subjects:

Probability Theory and Stochastic Processes.

Partial Differential Equations.

Group Theory and Generalizations.

Potential Theory.

Physical Description:

1 online resource (VIII, 268 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1999.

System Details:

text file PDF

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, id est, 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.

Contents:

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.

Other Format:

Printed edition:

ISBN:

9783540480761

Access Restriction:

Restricted for use by site license.