Interior regularity of the degenerate Monge-Ampère equation

DOI10.1017/S0004972700037436zbMath1067.35028OpenAlexW2128832394MaRDI QIDQ4470026

Zbigniew Błocki

Publication date: 22 June 2004

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0004972700037436

zbMATH Keywords

interior regularitydegenerate Monge-Ampère equation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear elliptic equations (35J60) Degenerate elliptic equations (35J70)

Related Items (8)

On Neumann problem for the degenerate Monge-Ampère type equations ⋮ The degenerate Monge-Ampère equations with the Neumann condition ⋮ Interior \(W^{2, p}\) estimate for small perturbations to the complex Monge-Ampère equation ⋮ Pogorelov estimates for the Monge–Ampère equations ⋮ On the regularity of the complex Monge-Ampère equations ⋮ The complex Monge-Ampère equation on compact Kähler manifolds ⋮ A gradient estimate in the Calabi-Yau theorem ⋮ Pogorelov type \(C^2\) estimates for sum Hessian equations and a rigidity theorem

Cites Work

• \(C^ 2\) a priori estimates for degenerate Monge-Ampère equations
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• On the Dirichlet problem for degenerate Monge-Ampère equations.
• Regularity of generalized solutions of Monge-Ampère equations
• Interior regularity of the complex Monge-Ampère equation in convex domains
• Regularity of the pluricomplex Green function with several poles
• The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
• Differential equations on riemannian manifolds and their geometric applications
• On the regularity of the monge-ampère equation det (∂2 u/∂xi ∂xj) = f(x, u)
• Some Counterexamples to the Regularity of Monge-Ampere Equations
• Smooth exhaustion functions in convex domains
• On the existence of a complete Kähler metric on non-compact complex manifolds and the regularity of fefferman's equation
• The \(C^{1,1}\) regularity of the pluricomplex Green function

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