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

• Main Author: Eberle, Andreas (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1999.
• Edition: 1st ed. 1999.
• Series: Lecture Notes in Mathematics, 1718
• Subjects: Probabilities.; Partial differential equations.; Group theory.; Potential theory (Mathematics).; Probability Theory and Stochastic Processes.; Partial Differential Equations.; Group Theory and Generalizations.; Potential Theory.
• Physical Description: VIII, 268 p. online resource.
• ISBN: 9783540480761
• ISSN: 0075-8434 ;
• DOI: 10.1007/BFb0103045

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.