Extension and trace for nonlocal operators
Analysis of PDEs
2018-12-04 v2 Probability
Abstract
We prove an optimal extension and trace theorem for Sobolev spaces of nonlocal operators. The extension is given by a suitable Poisson integral and solves the corresponding nonlocal Dirichlet problem. We give a Douglas-type formula for the quadratic form of the Poisson extension.
Cite
@article{arxiv.1710.05880,
title = {Extension and trace for nonlocal operators},
author = {Krzysztof Bogdan and Tomasz Grzywny and Katarzyna Pietruska-Pałuba and Artur Rutkowski},
journal= {arXiv preprint arXiv:1710.05880},
year = {2018}
}
Comments
We are now able to add the trace theorem and complete the picture