Removable sets and Lp-uniqueness on manifolds and metric measure spaces
Hinz, M.; Masamune, J.; Suzuki, K.
Dr Kohei Suzuki email@example.com
We study symmetric diffusion operators on metric measure spaces. Our main question is whether essential self-adjointness or -uniqueness are preserved under the removal of a small closed set from the space. We provide characterizations of the critical size of removed sets in terms of capacities and Hausdorff dimension without any further assumption on removed sets. As a key tool we prove a non-linear truncation result for potentials of nonnegative functions. Our results are robust enough to be applied to Laplace operators on general Riemannian manifolds as well as sub-Riemannian manifolds and metric measure spaces satisfying curvature-dimension conditions. For non-collapsing Ricci limit spaces with two-sided Ricci curvature bounds we observe that the self-adjoint Laplacian is already fully determined by the classical Laplacian on the regular part.
Hinz, M., Masamune, J., & Suzuki, K. (2023). Removable sets and Lp-uniqueness on manifolds and metric measure spaces. Nonlinear Analysis: Theory, Methods and Applications, 234, https://doi.org/10.1016/j.na.2023.113296
|Journal Article Type||Article|
|Acceptance Date||Apr 18, 2023|
|Online Publication Date||May 13, 2023|
|Deposit Date||May 17, 2023|
|Publicly Available Date||May 17, 2023|
|Peer Reviewed||Peer Reviewed|
Published Journal Article
Publisher Licence URL
© 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license<br /> (http://creativecommons.org/licenses/by/4.0/).