Boundary behavior of \(k\)-convex solutions for singular \(k\)-Hessian equations

DOI10.1016/j.na.2018.06.010zbMath1401.35087OpenAlexW2876014120MaRDI QIDQ1791724

Huayuan Sun, Mei-Qiang Feng

Publication date: 11 October 2018

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2018.06.010

zbMATH Keywords

Dirichlet condition\(k\)-convex solutionssingular \(k\)-Hessian equations

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Monge-Ampère equations (35J96)

Related Items (12)

Non-degeneracy and uniqueness of the radial solutions to a coupled \(k\)-Hessian system ⋮ Existence and uniqueness of nontrivial radial solutions for \(k\)-Hessian equations ⋮ Analysis of nontrivial radial solutions for singular superlinear \(k\)-Hessian equations ⋮ The existence and multiplicity of \(k\)-convex solutions for a coupled \(k\)-Hessian system ⋮ Existence and asymptotic behavior of strictly convex solutions for singular \(k\)-Hessian equations with nonlinear gradient terms ⋮ Existence of positive solutions for a singular Hessian equation with a negative augmented term ⋮ 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 a singular \(k\)-Hessian equation ⋮ On a \(k\)-Hessian equation with a weakly superlinear nonlinearity and singular weights ⋮ Optimal global asymptotic behavior of the solution to a singular Monge-Ampère equation ⋮ The existence and asymptotic behavior of boundary blow-up solutions to the \(k\)-Hessian equation

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