Uniqueness and Non-Uniqueness of Semigroups Generated by Singular Diffusion Operators : Lecture Notes in Mathematics - Andreas Eberle

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

By: Andreas Eberle

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Paperback | 17 November 1999

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276 Pages

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23.5 x 15.24 x 1.91

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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.

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