Uniqueness and Non-Uniqueness of Semigroups Generated by Singular Diffusion Operators / Edition 1

by Andreas Eberle

Overview

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.

Product Details

ISBN-13:	9783540666288
Publisher:	Springer Berlin Heidelberg
Publication date:	01/14/2000
Series:	Lecture Notes in Mathematics , #1718
Edition description:	1999
Pages:	268
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

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.