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

Eberle, Andreas

ISBN 10: 3540666281 / ISBN 13: 9783540666288

Editore: Springer 1999-11, 1999

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Codice articolo 6666-IUK-9783540666288

Dati bibliografici

• Titolo: Uniqueness and Non-Uniqueness of Semigroups Generated by Singular Diffusion Operators
• Editore: Springer 1999-11
• Data di pubblicazione: 1999
• Lingua: Inglese
• ISBN 10: 3540666281
• ISBN 13: 9783540666288
• Rilegatura: PF
• Condizione: New

Descrizione articolo

Riassunto

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.

Contenuti

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.