%0 eBook %M Solr-EB000658333 %A Eberle, Andreas %I Springer Berlin Heidelberg %D 1999 %C Berlin, Heidelberg %G English %B Lecture Notes in Mathematics %@ 9783540480761 %T Uniqueness and Non-Uniqueness of Semigroups Generated by Singular Diffusion Operators %U https://doi.org/10.1007/BFb0103045?nosfx=y %7 1st ed. 1999 %X 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