Sharp conditions for the existence of boundary blow-up solutions to the Monge-Ampère equation

DOI10.1007/s00526-018-1312-3zbMath1410.35051OpenAlexW2785820875WikidataQ115387267 ScholiaQ115387267MaRDI QIDQ1751568

Yihong Du, Xuemei Zhang

Publication date: 25 May 2018

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-018-1312-3

zbMATH Keywords

Monge-Ampère equationblow upstrictly convex solutions

Mathematics Subject Classification ID

Blow-up in context of PDEs (35B44) Monge-Ampère equations (35J96)

Related Items (37)

Entire positive \(k\)-convex solutions to \(k\)-Hessian type equations and systems ⋮ Convex solutions of Monge-Ampère equations and systems: existence, uniqueness and asymptotic behavior ⋮ The existence and blow-up of the radial solutions of a \((k_1, k_2)\)-Hessian system involving a nonlinear operator and gradient ⋮ Existence and uniqueness of nontrivial radial solutions for \(k\)-Hessian equations ⋮ Analysis of nontrivial radial solutions for singular superlinear \(k\)-Hessian equations ⋮ Existence and boundary asymptotic behavior of strictly convex solutions for singular Monge-Ampère problems with gradient terms ⋮ Boundary blow-up solutions to singular \(k\)-Hessian equations with gradient terms: sufficient and necessary conditions and asymptotic behavior ⋮ Nontrivial solutions for the polyharmonic problem: existence, multiplicity and uniqueness ⋮ The optimal global estimates and boundary behavior for large solutions to the \(k\)-Hessian equation ⋮ Existence and asymptotic behavior of strictly convex solutions for singular \(k\)-Hessian equations with nonlinear gradient terms ⋮ Necessary and sufficient conditions for the existence of entire subsolutions to \(p\)-\(k\)-Hessian equations ⋮ The existence of infinitely many boundary blow-up solutions to the \(p\)-\(k\)-Hessian equation ⋮ Eigenvalue problems for singular \(p\)-Monge-Ampère equations ⋮ Sufficient and necessary conditions on the existence and estimates of boundary blow-up solutions for singular \(p\)-Laplacian equations ⋮ A class of singular \(k_{i}\)-Hessian systems ⋮ Radial solutions of a nonlinear \(k\)-Hessian system involving a nonlinear operator ⋮ Strictly convex solutions for singular Monge-Ampère equations with nonlinear gradient terms: existence and boundary asymptotic behavior ⋮ Refined second boundary behavior of the unique strictly convex solution to a singular Monge-Ampère equation ⋮ New results of coupled system of \(k\)-Hessian equations ⋮ On Monge-Ampère equations with nonlinear gradient terms -- infinite boundary value problems ⋮ Boundary blow-up solutions to the \(k\)-Hessian equation with a weakly superlinear nonlinearity ⋮ On a singular \(k\)-Hessian equation ⋮ Boundary blow-up solutions to the Monge-Ampère equation: sharp conditions and asymptotic behavior ⋮ On a \(k\)-Hessian equation with a weakly superlinear nonlinearity and singular weights ⋮ Boundary blow-up solutions to the \(k\)-Hessian equation with singular weights ⋮ Boundary behavior of \(k\)-convex solutions for singular \(k\)-Hessian equations ⋮ Optimal global asymptotic behavior of the solution to a singular Monge-Ampère equation ⋮ Entire large solutions to the \(k\)-Hessian equations with weights: existence, uniqueness and asymptotic behavior ⋮ 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 blow-up solutions to the \(k\)-Hessian equation with the logarithmic nonlinearity and singular weights ⋮ Blow-up solutions to the Monge-Ampère equation with a gradient term: sharp conditions for the existence and asymptotic estimates ⋮ A class of singular coupled systems of superlinear Monge-Ampère equations ⋮ Asymptotic boundary estimates for solutions to the \(p\)-Laplacian with infinite boundary values ⋮ Positive solutions to second-order singular nonlocal problems: existence and sharp conditions ⋮ On a power-type coupled system of k-Hessian equations

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