Abstract
We investigate the Markov process on the boundary of a bounded Lipschitz domain associated to the Neumann and Robin boundary value problems. We first construct Lp-semigroups of sub-Markovian contractions on the boundary, generated by the boundary conditions, and we show that they are induced by the transition functions of the forthcoming processes. As in the smooth boundary case the process on the boundary is obtained by the time change with the inverse of a continuous additive functional of the reflected Brownian motion. The Robin problem is treated with a Kato type Lp-perturbation method, using the Revuz correspondence. An exceptional (polar) set occurs on the boundary. We make the link with the Dirichlet forms approach.
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.
