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AuthorEberle, Andreas. author
TitleUniqueness and Non-Uniqueness of Semigroups Generated by Singular Diffusion Operators [electronic resource] / by Andreas Eberle
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1999
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Descript VIII, 268 p. online resource


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


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


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