Generalizing Dirichlet-to-Neumann operators
Probability
2022-02-23 v1
Abstract
The aim of this paper is to study the Dirichlet-to-Neumann operators in the context of Dirichlet forms and especially to figure out their probabilistic counterparts. Regarding irreducible Dirichlet forms, we will show that the Dirichlet-to-Neumann operators for them are associated with the trace Dirichlet forms corresponding to the time changed processes on the boundary. Furthermore, the Dirichlet-to-Neumann operators for perturbations of Dirichlet forms will be also explored. It turns out that for typical cases such a Dirichlet-to-Neumann operator corresponds to a quasi-regular positivity preserving (symmetric) coercive form, so that there exists a family of Markov processes associated with it via Doob's -transformations.
Cite
@article{arxiv.2202.10914,
title = {Generalizing Dirichlet-to-Neumann operators},
author = {Liping Li},
journal= {arXiv preprint arXiv:2202.10914},
year = {2022}
}