Boundary behavior of large solutions to the Monge-Ampère equations with weights

DOI10.1016/j.jde.2015.03.040zbMath1318.35061OpenAlexW1975648590MaRDI QIDQ2347025

Zhijun Zhang

Publication date: 26 May 2015

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

Full work available at URL: https://doi.org/10.1016/j.jde.2015.03.040

zbMATH Keywords

boundary behaviorMonge-Ampère equationsstrictly convex large solutions

Mathematics Subject Classification ID

Monge-Ampère equations (35J96)

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Cites Work

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• Boundary asymptotical behavior of large solutions to complex Hessian equations
• Keller-Osserman type conditions for some elliptic problems with gradient terms
• Large solutions to complex Monge-Ampère equations: existence, uniqueness and asymptotics
• On the inequality \(\Delta u \geqq f (u)\)
• Boundary behavior for large solutions to elliptic equations with singular weights
• Large solutions of elliptic equations with a weakly superlinear nonlinearity
• Blow-up rates of large solutions for elliptic equations
• 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
• Boundary blow-up problems for Hessian equations
• Asymptotic behavior of solutions of boundary blow-up problems
• Semilinear elliptic equations with uniform blow-up on the boundary
• `Large' solutions of semilinear elliptic equations: Existence, uniqueness and asymptotic behaviour
• The Monge-Ampère equation with infinite boundary value
• Uniqueness of the blow-up boundary solution of logistic equations with absorbtion.
• On singular boundary value problems for the Monge-Ampère operator
• On the blow-up boundary solutions of the Monge-Ampére equation with singular weights
• Regular variation and differential equations
• 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
• On solutions of δu=f(u)
• Necessary and sufficient conditions on solvability for Hessian inequalities
• 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
• 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)
• Blow-Up Solutions for a Class of Semilinear Elliptic and Parabolic Equations
• 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
• Explosive solutions of quasilinear elliptic equations: existence and uniqueness
• Hessian equations with infinite Dirichlet boundary
• Convexity and asymptotic estimates for large solutions of Hessian equations
• The Monge-Ampère equation
• The Bieberbach-Rademacher problem for the Monge-Ampère operator