The Dirichlet problem for a complex Hessian equation on compact Hermitian manifolds with boundary

Abstract

We solve the classical Dirichlet problem for a general complex Hessian equation on a small ball in C-n. Then, we show that there is a continuous solution, in pluripotential theory sense, to the Dirichlet problem on compact Hermitian manifolds with boundary that equipped locally conformal Kahler metrics, provided a subsolution.