The optimal global estimates and boundary behavior for large solutions to the \(k\)-Hessian equation

DOI10.1007/S11464-020-0045-8zbMath1526.35164arXiv2004.12640OpenAlexW4361297392MaRDI QIDQ6058340

Haitao Wan, Yongxiu Shi

Publication date: 1 November 2023

Published in: Frontiers of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.12640

zbMATH Keywords

existenceasymptotic behaviorboundary blow-up problem\(k\)-Hessian equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear elliptic equations (35J60) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Monge-Ampère equations (35J96)

Cites Work

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• Existence and nonexistence theorem for entire subsolutions of \(k\)-Yamabe type equations
• On the inequality \(\Delta u \geqq f (u)\)
• Boundary asymptotic and uniqueness of solutions to the \(p\)-Laplacian with infinite boundary values
• Nonexistence of positive solutions for some fully nonlinear elliptic equations
• Boundary asymptotical behavior of large solutions to Hessian equations
• The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian
• 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
• On the Dirichlet problem for Hessian equations
• Elliptic partial differential equations of second order
• Optimal boundary regularity for a singular Monge-Ampère equation
• Sharp conditions for the existence of boundary blow-up solutions to the Monge-Ampère equation
• 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
• A unified boundary behavior of large solutions to Hessian equations
• Existence and boundary asymptotic behavior of large solutions of Hessian equations
• Optimal global and boundary asymptotic behavior of large solutions to the Monge-Ampère equation
• Boundary behavior of large solutions to the Monge-Ampère equation in a borderline case
• The existence and asymptotic behavior of boundary blow-up solutions to the \(k\)-Hessian equation
• Boundary behavior of large solutions to the Monge-Ampère equations with weights
• Large solutions to the Monge-Ampère equations with nonlinear gradient terms: existence and boundary behavior
• On the Monge-Ampère equation with boundary blow-up: existence, uniqueness and asymptotics
• 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
• The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
• On a problem of Bieberbach and Rademacher
• The dirichlet problem for a class of fully nonlinear elliptic equations
• 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
• Boundary blow-up solutions to the \(k\)-Hessian equation with singular weights
• Convexity and asymptotic estimates for large solutions of Hessian equations
• The Bieberbach-Rademacher problem for the Monge-Ampère operator

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