Hölder continuous solutions to complex Hessian equations

Abstract

We prove the Hölder continuity of the solution to complex Hessian equation with the right hand side in $L^p$, $p>\frac{n}{m}$, $1<m<n$, in a $m$-strongly pseudoconvex domain in ${\mathbb{C}}^n$ under some additional conditions on the density near the boundary and on the boundary data.

19 pages. Added Theorem 3.7: when the boundary is Holder continuous, there exists a Holder continuous $m$-sh extension to the domain

References in corpus (4)

• Viscosity solutions to complex Hessian equations
• Exponential estimates for plurisubharmonic functions and stochastic dynamics
• Hölder continuity of solutions to the complex Monge-Ampère equation with the right hand side in L^p. The case of compact Kähler manifolds
• Solutions to degenerate complex Hessian equations

Cited by in corpus (6)

• The Monge-Ampère equation for (n-1)-plurisubharmonic functions on a compact Kähler manifold
• $C^{2,\alpha }$ estimates for nonlinear elliptic equations in complex and almost complex geometry
• A variational Approach to complex Hessian equations in ${\mathbb{C}}^n$
• The Hölder continuous subsolution theorem for complex Hessian equations
• Nonsmooth viscosity solutions of elementary symmetric functions of the complex Hessian
• The Continuous Subsolution Problem for Complex Hessian Equations