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

Download or read book Uniqueness and Non-Uniqueness of Semigroups Generated by Singular Diffusion Operators written by Andreas Eberle and published by Springer. This book was released on 2007-01-05 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.