TY  - BOOK
AU  - Eberle,Andreas
ED  - SpringerLink (Online service)
TI  - Uniqueness and Non-Uniqueness of Semigroups Generated by Singular Diffusion Operators
T2  - Lecture Notes in Mathematics,
SN  - 9783540480761
AV  - QA273.A1-274.9 
U1  - 519.2 23
PY  - 1999///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Differential equations, partial
KW  - Potential theory (Mathematics)
KW  - Distribution (Probability theory)
KW  - Probability Theory and Stochastic Processes
KW  - Partial Differential Equations
KW  - Potential Theory
N1  - 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
N2  - 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
UR  - http://dx.doi.org/10.1007/BFb0103045
ER  -