12 citations · 20 across the 6 of their papers we have counts for
7 papers
Regularity of Degenerate Hessian Equation
Slawomir Dinew, Szymon Plis, Xiangwen Zhang
We show a second order a priori estimate for solutions to the complex -Hessian equation on a compact Kähler manifold provided the --st root of the right hand side is $\m…
An analytic proof of the Krylov estimates for the complex Monge-Ampere equation and applications
Slawomir Dinew, Szymon Plis
We provide an analytic proof of a theorem of Krylov dealing with global estimates to solutons of degenerate complex Monge-Ampère equations. As an application we show opti…
On regularization of plurisubharmonic functions near boundary points
Szymon Pliś
We prove in an elementary way that for a Lipschitz domain $D\subset \cn$, all plurisubharmonic functions on can be regularized near any boundary point.
Smooth Approximation of Plurisubharmonic Functions on Almost Complex Manifolds
F. Reese Harvey, H. Blaine Lawson, Szymon Pliś
This note establishes smooth approximation from above for J-plurisubharmonic functions on an almost complex manifold (X,J). The following theorem is proved. Suppose X is J-pseudoco…
The smoothing of -subharmonic functions
Szymon Pliś
We prove Richberg type theorem for -subharmonic function. The main tool is the complex Hessian equation for which we obtain the existence of the unique smooth solution in strict…
Squares of positive -forms
Zbigniew Blocki, Szymon Plis
We show that if is a positive -form then so is . We also prove that this is no longer true for forms of higher degree.
The Monge-Ampère equation on almost complex manifolds
Szymon Plis
We study the Dirichlet problem for the Monge-Ampère equation on almost complex manifolds. We obtain the existence of the unique smooth solution of this problem in strictly pseudoco…