Large solutions to the Monge-Ampère equations with nonlinear gradient terms: existence and boundary behavior

DOI10.1016/j.jde.2017.09.010zbMath1379.35157OpenAlexW2755404234MaRDI QIDQ2410311

Zhijun Zhang

Publication date: 17 October 2017

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2017.09.010

zbMATH Keywords

Monge-Ampère equationunique solvabilityboundary blow-upstrictly convex solutions

Mathematics Subject Classification ID

Blow-up in context of PDEs (35B44) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Monge-Ampère equations (35J96)

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Cites Work

• Unnamed Item
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• Exact boundary behavior of the unique positive solution to some singular elliptic problems
• On the inequality \(\Delta u \geqq f (u)\)
• Boundary asymptotical behavior of large solutions to Hessian equations
• Classical solvability of the Dirichlet problem for the Monge-Ampère equation
• Two remarks on Monge-Ampère equations
• Boundary behaviour of the complex Monge-Ampère equation
• The Dirichlet problem for a complex Monge-Ampère equation
• Nonlinear elliptic equations with singular boundary conditions and stochastic control with state constraints. I: The model problem
• Boundary blow-up problems for Hessian equations
• The Monge-Ampère equation with infinite boundary value
• Boundary blow up for semilinear elliptic equations with nonlinear gradient terms
• On singular boundary value problems for the Monge-Ampère operator
• Uniqueness of boundary blowup solutions to \(k\)-curvature equation
• On the blow-up boundary solutions of the Monge-Ampére equation with singular weights
• Regular variation and differential equations
• Boundary behavior of large solutions to the Monge-Ampère equations with weights
• On the Monge-Ampère equation with boundary blow-up: existence, uniqueness and asymptotics
• Solution to the boundary blowup problem for \(k\)-curvature equation
• The blow-up rate of solutions to boundary blow-up problems for the complex Monge-Ampère operator
• Boundary behavior of large solutions for semilinear elliptic equations with weights
• On solutions of δu=f(u)
• On the existence of solutions to the Monge-Ampère equation with infinite boundary values
• Some existence results for fully nonlinear elliptic equations of monge-ampère type
• On boundary blow-up problems for the complex Monge-Ampère equation
• Asymptotic Behaviour of the Gradient of Large Solutions to Some Nonlinear Elliptic Equations
• The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
• On the regularity of the monge-ampère equation det (∂2 u/∂xi ∂xj) = f(x, u)
• Asymptotic behaviour of large solutions of an elliptic quasilinear equation in a borderline case
• On the existence of a complete Kähler metric on non-compact complex manifolds and the regularity of fefferman's equation
• Pointwise 𝐶^{2,𝛼} estimates at the boundary for the Monge-Ampère equation
• Hessian equations with infinite Dirichlet boundary
• Regularly varying functions
• Convexity and asymptotic estimates for large solutions of Hessian equations
• The Monge-Ampère equation
• The Bieberbach-Rademacher problem for the Monge-Ampère operator