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Regularity of fully non-linear elliptic equations on Hermitian manifolds. II
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abstract
In this paper we investigate the regularity and solvability of solutions to Dirichlet problem for fully non-linear elliptic equations with gradient terms on Hermitian manifolds, which include among others the Monge-Amp\`ere equation for $(n-1)$-plurisubharmonic functions. Some significantly new features of regularity assumptions on the boundary and boundary data are obtained, which reveal how the shape of the boundary influences such regularity assumptions. Such new features follow from quantitative boundary estimates which specifically enable us to apply a blow-up argument to derive the gradient estimate. Interestingly, the subsolutions are constructed when the background space is moreover a product of a closed Hermitian manifold with a compact Riemann surface with boundary.
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Cited by 1 Pith paper
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Second order estimates for $\chi$-semi convex solutions of Hessian equations on Hermitian manifolds
For admissible, chi-semi-convex solutions of complex Hessian equations with gradient terms on compact Hermitian manifolds, the paper proves uniform second-order estimates.
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