On the existence of solutions of a class of Monge-Ampére equations

DOI10.1007/BF02560581zbMath0665.35027MaRDI QIDQ3816414

Tian, Gang

Publication date: 1988

Published in: Acta Mathematica Sinica (Search for Journal in Brave)

zbMATH Keywords

Dirichlet problemexistenceMonge-Ampère equationconvex bounded domain\(C^ 0\)-estimate

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear boundary value problems for linear elliptic equations (35J65) A priori estimates in context of PDEs (35B45)

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A third derivative estimate for Monge-Ampere equations with conic singularities ⋮ A continuity method to construct canonical metrics ⋮ The complex Hessian equations with gradient terms on Hermitian manifolds ⋮ New proof for the regularity of Monge-Ampère type equations ⋮ Some interior regularity estimates for solutions of complex Monge-Ampère equations on a ball ⋮ The parabolic Monge-Ampère equation on compact almost Hermitian manifolds ⋮ On the Dirichlet problem for a class of singular complex Monge-Ampère equations ⋮ On the limit behavior of metrics in the continuity method for the Kähler–Einstein problem on a toric Fano manifold ⋮ The \(C^{2,\alpha }\)-estimate for conical Kähler-Ricci flow ⋮ A \(\mathcal{C}^{2, \alpha}\) estimate of the complex Monge-Ampère equation ⋮ Some progresses on Kähler-Ricci flow ⋮ Second order estimates for complex Hessian equations on Hermitian manifolds ⋮ Kähler-Einstein metrics with edge singularities ⋮ \(C^{2,\alpha}\) regularities and estimates for nonlinear elliptic and parabolic equations in geometry

Cites Work

• Nonlinear elliptic systems with quadratic growth
• Sur les équations de Monge-Ampère. I
• Equazioni ellittiche del II\(^ \circ\) ordine e spazi \({\mathcal L}^{(2,\lambda)}\)
• The L\(^p\)-integrability of the partial derivatives of a quasiconformal mapping
• Improper affine hyperspheres of convex type and a generalization of a theorem by K. Jörgens
• Classical solutions of fully nonlinear, convex, second-order elliptic equations
• On the regularity of the monge-ampère equation det (∂2 u/∂xi ∂xj) = f(x, u)
• On the regularity of the solution of then-dimensional Minkowski problem
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