The exterior Dirichlet problem for the homogeneous complex \(k\)-Hessian equation
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Publication:2685126
DOI10.1515/ans-2022-0039OpenAlexW4315647935MaRDI QIDQ2685126
Xi-Nan Ma, Zhenghuan Gao, Dekai Zhang
Publication date: 19 February 2023
Published in: Advanced Nonlinear Studies (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2208.03794
Smoothness and regularity of solutions to PDEs (35B65) Boundary value problems for second-order elliptic equations (35J25) Nonlinear elliptic equations (35J60)
Cites Work
- Unnamed Item
- Regularity of the homogeneous Monge-Ampère equation
- A viscosity approach to degenerate complex Monge-Ampère equations
- The exterior Dirichlet problem for special Lagrangian equations in dimensions \(n\leq 4\)
- Solving the degenerate complex Monge-Ampère equation with one concentrated singularity
- The quermassintegral inequalities for \(k\)-convex starshaped domains
- Symmetries and other transformations of the complex Monge-Ampère equation
- The Dirichlet problem for the degenerate Monge-Ampère equation
- The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian
- The Dirichlet problem for Hessian equations on Riemannian manifolds
- Weak interior second order derivative estimates for degenerate nonlinear elliptic equations
- On the Dirichlet problem for degenerate Monge-Ampère equations.
- On the exterior Dirichlet problem for Hessian quotient equations
- On the Dirichlet problems for symmetric function equations of the eigenvalues of the complex Hessian
- The extremal function associated to intrinsic norms.
- Second-order estimates and regularity for fully nonlinear elliptic equations on Riemannian manifolds
- Minkowski inequalities via nonlinear potential theory
- A second order estimate for complex Hess equations on a compact Kähler manifold
- Monotonicity formulas in potential theory
- A variational approach to complex Hessian equations in \(\mathbb{C}^n\)
- Geometric aspects of \(p\)-capacitary potentials
- Inequalities for quermassintegrals on \(k\)-convex domains
- The exterior Dirichlet problem for fully nonlinear elliptic equations related to the eigenvalues of the Hessian
- Weak solutions to the complex Hessian equation.
- On the exterior Dirichlet problem for Hessian equations
- The Dirichlet Problem for Degenerate Hessian Equations
- The k-Hessian Equation
- The dirichlet problem for a class of fully nonlinear elliptic equations
- Some Counterexamples to the Regularity of Monge-Ampere Equations
- An extension to a theorem of Jörgens, Calabi, and Pogorelov
- A variational theory of the Hessian equation
- A family of higher-order isoperimetric inequalities
- On the exterior Dirichlet problem for special Lagrangian equations
- WEAK CONTINUITY OF THE COMPLEX -HESSIAN OPERATORS WITH RESPECT TO LOCAL UNIFORM CONVERGENCE
- On the Regularity of the Pluricomplex Green Functions
- Hessian Equations with Elementary Symmetric Functions