On the regularity of the complex Hessian equation

2021/10/06 by Ahag, Per, Czyz, Rafal
#31C45 #35B35 #35J60 #53C55 #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Primary 32U05 #Secondary 32Q26

paper · doi:10.48550/arxiv.2110.02620

Abstract

This note aims to investigate the regularity of a solution to the Dirichlet problem for the complex Hessian equation, which has a density of the m-Hessian measure that belongs to L^q, for q≤\frac nm.

Related

• A remark on the Hölder regularity of solutions to the complex Hessian equation
• The Dirichlet problem for the complex Hessian operator in the class N_m(H)
• Continuity of Solutions to Complex Hessian Equations via the Dinew-Kołodziej Estimate
• Trace Inequalities, isocapacitary inequalities and regularity of the complex Hessian equations
• Regularity of Degenerate Hessian Equation