Continuity of solutions to complex Hessian equations via the Dinew–Kołodziej estimate

This study extends the celebrated volume-capacity estimates of Dinew and Kołodziej, providing a foundation for examining the regularity of solutions to boundary value problems for complex Hessian equations. By integrating the techniques established by Dinew and Kołodziej and incorporating recent advances by Charabati and Zeriahi, we demonstrate the continuity of the solutions.