scholarly journals Hessian estimates for convex solutions to quadratic Hessian equation

2019 ◽  
Vol 36 (2) ◽  
pp. 451-454 ◽  
Author(s):  
Matt McGonagle ◽  
Chong Song ◽  
Yu Yuan
Keyword(s):  
Hessian Equation ◽  
Hessian Estimates

The Dirichlet problem for the complex Hessian operator in the class $\mathcal{N}_m(\Omega,f)$

2021 ◽  
Vol 127 (2) ◽  
pp. 287-316
Author(s):  
Ayoub El Gasmi
Keyword(s):  
Weak Solution ◽  
Dirichlet Problem ◽  
Borel Measure ◽  
Positive Borel Measure ◽  
Hessian Equation ◽  
Hessian Operator ◽  
Hyperconvex Domain ◽  
Complex Hessian Operator

Let $\Omega\subset \mathbb{C}^{n}$ be a bounded $m$-hyperconvex domain, where $m$ is an integer such that $1\leq m\leq n$. Let $\mu$ be a positive Borel measure on $\Omega$. We show that if the complex Hessian equation $H_m (u) = \mu$ admits a (weak) subsolution in $\Omega$, then it admits a (weak) solution with a prescribed least maximal $m$-subharmonic majorant in $\Omega$.

scholarly journals Bounded solutions of a k-Hessian equation in a ball

2016 ◽  
Vol 261 (1) ◽  
pp. 797-820 ◽  
Author(s):  
Justino Sánchez ◽  
Vicente Vergara
Keyword(s):  
Bounded Solutions ◽  
Hessian Equation

On a singular k-Hessian equation

2019 ◽  
Vol 97 ◽  
pp. 60-66 ◽  
Author(s):  
Xuemei Zhang
Keyword(s):  
Hessian Equation

Weighted Orlicz regularity estimates for fully nonlinear elliptic equations with asymptotic convexity

2019 ◽  
Vol 21 (04) ◽  
pp. 1850024 ◽  
Author(s):  
Mikyoung Lee
Keyword(s):  
Elliptic Equations ◽  
Nonlinear Operator ◽  
Orlicz Spaces ◽  
Nonlinear Elliptic Equations ◽  
Fully Nonlinear Elliptic Equations ◽  
Fully Nonlinear ◽  
Nonlinear Elliptic ◽  
Regularity Estimates ◽  
Hessian Estimates ◽  
Asymptotic Convexity

We prove interior Hessian estimates in the setting of weighted Orlicz spaces for viscosity solutions of fully nonlinear, uniformly elliptic equations [Formula: see text] under asymptotic assumptions on the nonlinear operator [Formula: see text] The results are further extended to fully nonlinear, asymptotically elliptic equations.

Iterative properties of solution for a general singular n-Hessian equation with decreasing nonlinearity

2021 ◽  
Vol 112 ◽  
pp. 106826
Author(s):  
Xinguang Zhang ◽  
Jiqiang Jiang ◽  
Yonghong Wu ◽  
Benchawan Wiwatanapataphee
Keyword(s):  
Hessian Equation
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