Continuity of Solutions to Complex Hessian Equations via the Dinew-Ko{\l}odziej Estimate

TL;DR

This paper extends key volume-capacity estimates for complex Hessian equations, enabling the demonstration of solution continuity by integrating previous techniques with recent advances.

Contribution

It generalizes the Dinew-Ko{ }lodziej estimates and applies them to establish the continuity of solutions to complex Hessian boundary value problems.

Findings

Extended volume-capacity estimates for complex Hessian equations.

Proved continuity of solutions under new estimates.

Integrated recent advances to strengthen regularity results.

Abstract

This study extends the celebrated volume-capacity estimates of Dinew and Kolodziej, 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 Kolodziej and incorporating recent advances by Charabati and Zeriahi, we demonstrate the continuity of the solutions.