A unified boundary behavior of large solutions to Hessian equations

DOI10.1007/s11401-020-0220-yzbMath1448.35204OpenAlexW3044218926MaRDI QIDQ2193014

Zhijun Zhang

Publication date: 24 August 2020

Published in: Chinese Annals of Mathematics. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11401-020-0220-y

zbMATH Keywords

boundary behaviorHessian equationsstrictly \(k\)-convex large solutions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear elliptic equations (35J60)

Related Items (3)

Boundary blow-up solutions to singular \(k\)-Hessian equations with gradient terms: sufficient and necessary conditions and asymptotic behavior ⋮ The optimal global estimates and boundary behavior for large solutions to the \(k\)-Hessian equation ⋮ Boundary behavior of large solutions to the Monge-Ampère equation in a borderline case

Cites Work

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• On the inequality \(\Delta u \geqq f (u)\)
• Nonexistence of positive solutions for some fully nonlinear elliptic equations
• Existence of entire positive \(k\)-convex radial solutions to Hessian equations and systems with weights
• 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 blow-up problems for Hessian equations
• Asymptotic behavior of solutions of boundary blow-up problems
• `Large' solutions of semilinear elliptic equations: Existence, uniqueness and asymptotic behaviour
• The Monge-Ampère equation with infinite boundary value
• 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
• 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
• Boundary behavior of large solutions for semilinear elliptic equations with weights
• Metasolutions of Parabolic Equations in Population Dynamics
• 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
• 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)
• Liouville property and regularity of a Hessian quotient equation
• On the existence of a complete Kähler metric on non-compact complex manifolds and the regularity of fefferman's equation
• 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

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