Boundary blow-up solutions to the Monge-Ampère equation: sharp conditions and asymptotic behavior

DOI10.1515/ANONA-2020-0023zbMath1466.35237OpenAlexW2964432218MaRDI QIDQ2027094

Xuemei Zhang, Mei-Qiang Feng

Publication date: 21 May 2021

Published in: Advances in Nonlinear Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/anona-2020-0023

zbMATH Keywords

asymptotic behaviorMonge-Ampère equationboundary blow upexistence of strictly convex solutions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Blow-up in context of PDEs (35B44) Monge-Ampère equations (35J96)

Related Items (18)

The exterior Dirichlet problems of Monge-Ampère equations in dimension two ⋮ The first initial-boundary value problem of parabolic Monge-Ampère equations outside a bowl-shaped domain ⋮ Radial solutions for fully nonlinear elliptic equations of Monge-Ampère type ⋮ Entire positive \(k\)-convex solutions to \(k\)-Hessian type equations and systems ⋮ New results of positive doubly periodic solutions to telegraph equations ⋮ Convex solutions of Monge-Ampère equations and systems: existence, uniqueness and asymptotic behavior ⋮ Existence and uniqueness of nontrivial radial solutions for \(k\)-Hessian equations ⋮ Global existence of solution for Monge-Ampére equation with an external periodic force on 3-dimensional torus ⋮ Existence and boundary asymptotic behavior of strictly convex solutions for singular Monge-Ampère problems with gradient terms ⋮ The existence and multiplicity of \(k\)-convex solutions for a coupled \(k\)-Hessian system ⋮ The existence of radial \(k\)-admissible solutions for \(n\)-dimension system of \(k\)-Hessian equations ⋮ Eigenvalue problems for singular \(p\)-Monge-Ampère equations ⋮ \(k\)-convex solutions for multiparameter Dirichlet systems with \(k\)-Hessian operator and Lane-Emden type nonlinearities ⋮ Strictly convex solutions for singular Monge-Ampère equations with nonlinear gradient terms: existence and boundary asymptotic behavior ⋮ On a \(k\)-Hessian equation with a weakly superlinear nonlinearity and singular weights ⋮ Positive solutions to second-order singular nonlocal problems: existence and sharp conditions ⋮ On a power-type coupled system of k-Hessian equations ⋮ Boundary behavior of large solutions to a class of Hessian equations

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