Abstract
Using conditional Brownian motion and the transformation of drift formula (of Cameron-Martin, Girsarov, Maruyama) we give integral conditions on a vector fieldb which imply the harmonic measures and Green functions for 1/2Δ and 1/2Δ+b(·)·∇ on a bounded Lipschitz domainD are equivalent. By equivalent we mean there exist two-sided inequalities with constants depending only onb andD. This enables one to conclude the potential theory for 1/2Δ+b(·)·∇ onD and 1/2Δ onD are the same.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
