Maximal \(m\)-subharmonic functions and the Cegrell class \(\mathcal{N}_m\)

DOI10.1016/j.indag.2019.03.005zbMath1425.32029OpenAlexW2924650211MaRDI QIDQ2422276

van Thien Nguyen

Publication date: 18 June 2019

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.indag.2019.03.005

zbMATH Keywords

maximal function\(m\)-subharmonic functionscomplex Hessian equationsCegrell class

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions on other spaces (31C05) Plurisubharmonic functions and generalizations (32U05)

Related Items

On the regularity of the complex Hessian equation, A note on the space of delta \(m\)-subharmonic functions, Continuous solutions to the complex \(m\)-Hessian type equation on strongly \(m\)-pseudoconvex domains in \(\mathbb{C}^n\), Solutions to weighted complex \(m\)-Hessian equations on domains in \(\mathbb{C}^n\), Capacity and stability on some Cegrell classes of \(m\)-subharmonic functions, Hölder continuity for solutions of the complex Hessian type equation, Complex Hessian-type equations in the weighted \(m\)-subharmonic class, Weak solutions to complex Hessian type equations in the class \(\mathcal{E}_{\phi}(X, \omega, m)\), Approximation of \(m\)-subharmonic function with given boundary values, On pluripotential theory associated to quaternionic \(m\)-subharmonic functions, Hessian boundary measures, Complex Hessian operator associated to an \(m\)-positive closed current and weighted \(m\)-capacity, Weak solutions to the complex \(m\)-Hessian type equation on open subsets of \(\mathbb{C}^n\), On a family of quasimetric spaces in generalized potential theory, Decay near boundary of volume of sublevel sets of \(m\)-subharmonic functions, On the weighted \(m\)-energy classes, Weak solutions to the complex \(m\)-Hessian type equations for arbitrary nonnegative Radon measures on open subsets of \(\mathbb{C}^n\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Capacities and Hessians in the class of \(m\)-subharmonic functions
• Solutions to degenerate complex Hessian equations
• Hölder continuous solutions to complex Hessian equations
• Monge-Ampère measures on pluripolar sets
• The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian
• Pluricomplex energy
• On a constant in the energy estimate
• On the Dirichlet problems for symmetric function equations of the eigenvalues of the complex Hessian
• Viscosity solutions to complex Hessian equations
• A variational approach to complex Hessian equations in \(\mathbb{C}^n\)
• A Dirichlet problem for the complex Monge-Ampère operator in \(\mathcal F(f)\)
• A priori estimates for complex Hessian equations
• Weak solutions to the complex Hessian equation.
• On delta $m$-subharmonic functions
• Liouville and Calabi-Yau type theorems for complex Hessian equations
• On a Monge–Ampère type equation in the Cegrell class E_χ
• The complex Monge–Ampère operator
• APPROXIMATION OF NEGATIVE PLURISUBHARMONIC FUNCTIONS WITH GIVEN BOUNDARY VALUES
• A comparison principle for the complex Monge-Ampère operator in Cegrell’s classes and applications
• A general Dirichlet problem for the complex Monge–Ampère operator
• The k-Hessian Equation
• The convexity of radially symmetric m-subharmonic functions
• A characterization of the Cegrell classes and generalized $m$-capacities
• Continuity of the complex Monge-Ampère operator
• Hessian measures on m-polar sets and applications to the complex Hessian equations
• Extension and approximation ofm-subharmonic functions
• Subsolution theorem for the complex Hessian equation