Nonlinear nonlocal Douglas identity
Analysis of PDEs
2023-01-12 v2 Functional Analysis
Probability
Abstract
We give Hardy-Stein and Douglas identities for nonlinear nonlocal Sobolev-Bregman integral forms with unimodal L\'evy measures. We prove that the corresponding Poisson integral defines an extension operator for the Sobolev-Bregman spaces. We also show that the Poisson integrals are quasiminimizers of the Sobolev-Bregman forms.
Cite
@article{arxiv.2006.01932,
title = {Nonlinear nonlocal Douglas identity},
author = {Krzysztof Bogdan and Tomasz Grzywny and Katarzyna Pietruska-Pałuba and Artur Rutkowski},
journal= {arXiv preprint arXiv:2006.01932},
year = {2023}
}
Comments
29 pages; we added applications to the Dirichlet-to-Neumann map, in Section 6