On the existence of solutions to the Monge-Ampère equation with infinite boundary values

DOI10.1090/S0002-9939-06-08623-0zbMath1172.35019OpenAlexW2061241797MaRDI QIDQ3419981

Ahmed Mohammed

Publication date: 1 February 2007

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-06-08623-0

zbMATH Keywords

Monge-Ampère equationstrictly convex domaininfinite boundary values

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear elliptic equations (35J60) Boundary values of solutions to elliptic equations and elliptic systems (35J67)

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Convex solutions of Monge-Ampère equations and systems: existence, uniqueness and asymptotic behavior ⋮ Asymptotic behaviour of Hessian equation with boundary blow up ⋮ Large solutions to the Monge-Ampère equations with nonlinear gradient terms: existence and boundary behavior ⋮ 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 ⋮ The optimal global estimates and boundary behavior for large solutions to the \(k\)-Hessian equation ⋮ Existence of entire positive \(k\)-convex radial solutions to Hessian equations and systems with weights ⋮ Necessary and sufficient conditions for the existence of entire subsolutions to \(p\)-\(k\)-Hessian equations ⋮ A unified boundary behavior of large solutions to Hessian equations ⋮ 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 necessary and sufficient condition for the existence of entire large solutions to a \(k\)-Hessian system ⋮ The iterative properties of solutions for a singular k-Hessian system ⋮ Radial solutions of a nonlinear \(k\)-Hessian system involving a nonlinear operator ⋮ On boundary blow-up problems for the complex Monge-Ampère equation ⋮ 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 ⋮ Sharp conditions for the existence of boundary blow-up solutions to the Monge-Ampère equation ⋮ Existence and boundary asymptotic behavior of large solutions of Hessian equations ⋮ Boundary blow-up solutions to the \(k\)-Hessian equation with singular weights ⋮ 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 ⋮ Unnamed Item ⋮ 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 ⋮ 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 ⋮ Boundary behavior of large solutions to the Monge-Ampère equations with weights ⋮ Boundary behavior of large solutions to a class of Hessian equations

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