Document Type
Article
Publication Date
8-2024
Keywords
Maximal estimates; ∂-Neumann operator; q-convexity
Abstract
It is well known that elliptic estimates fail for the ∂-Neumann problem. Instead, the best that one can hope for is that derivatives in every direction but one can be estimated by the associated Dirichlet form, and when this happens, we say that the ∂-Neumann problem satisfies maximal estimates. In the pseudoconvex case, a necessary and sufficient geometric condition for maximal estimates has been derived by Derridj (for (0, 1)-forms) and Ben Moussa (for (0, q)-forms when q ≥ 1). In this paper, we explore necessary conditions and sufficient conditions for maximal estimates in the non-pseudoconvex case. We also discuss when the necessary conditions and sufficient conditions agree and provide examples. Our results subsume the earlier known results from the pseudoconvex case.
Citation
Harrington, P. S., & Raich, A. (2024). Maximal Estimates for the ∂-Neumann Problem on Non-pseudoconvex Domains. Journal of Geometric Analysis, 34 (8), 237. https://doi.org/10.1007/s12220-024-01684-9
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
