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

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

byAndreas Eberle

Paperback | November 17, 1999

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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.
Title:Uniqueness and Non-Uniqueness of Semigroups Generated by Singular Diffusion OperatorsFormat:PaperbackDimensions:270 pagesPublished:November 17, 1999Publisher:Springer Berlin HeidelbergLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3540666281

ISBN - 13:9783540666288

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Table of 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.