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

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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.

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