Continuity of Solutions to Complex Hessian Equations via the Dinew-Kołodziej Estimate

2024/09/25 by Åhag, Per, Czyż, Rafał
#35B35 #35B65 #35J60 #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics #Primary 31C45 #Secondary 32U05

paper · doi:10.48550/arxiv.2409.16848

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.

Related

• A remark on the Hölder regularity of solutions to the complex Hessian equation
• On the regularity of the complex Hessian equation
• Modulus of continuity of solutions to complex Hessian equations
• Continuity of solutions to complex Hessian equations on compact Hermitian manifolds
• The weak solutions to complex Hessian equations