The Dirichlet problem for complex k-Hessian equations on compact Hermitian manifolds with boundary is solved under the assumption that a smooth subsolution exists.
Second order estimates for complex Hessian equations on Hermitian manifolds
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We derive second order estimates for $\chi$-plurisubharmonic solutions of complex Hessian equations with right hand sides depending on gradients on compact Hermitian manifolds.
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The Dirichlet Problem for the $k$-Hessian Equation on a complex manifold
The Dirichlet problem for complex k-Hessian equations on compact Hermitian manifolds with boundary is solved under the assumption that a smooth subsolution exists.