On the regularity of Dirichlet problem for fully non-linear elliptic equations on Hermitian manifolds
Abstract
We derive the solvability and regularity of the Dirichlet problem for fully non-linear elliptic equations possibly with degenerate right-hand side on Hermitian manifolds, through establishing a quantitative version of boundary estimate under a subsolution assumption. In addition, we construct the subsolution when the background manifold is a product of a closed Hermitian manifold with a compact Riemann surface with boundary.
Keywords
Cite
@article{arxiv.2203.04898,
title = {On the regularity of Dirichlet problem for fully non-linear elliptic equations on Hermitian manifolds},
author = {Rirong Yuan},
journal= {arXiv preprint arXiv:2203.04898},
year = {2022}
}
Comments
The main context of this paper is the integration of [arXiv:2203.03439] and the first parts of [arXiv:2001.09238] and [arXiv:2106.14837], while the second parts ofthe posts [arXiv:2001.09238, arXiv:2106.14837] are reorganized into another paper. More precisely, this paper is essentially extracted from [arXiv:2203.03439], Sections 4-6 in [arXiv:2001.09238] and Section 3 in [arXiv:2106.14837]