Convex solutions of Monge-Ampère equations and systems: existence, uniqueness and asymptotic behavior

DOI10.1515/anona-2020-0139zbMath1465.35262OpenAlexW3081422257MaRDI QIDQ831048

Mei-Qiang Feng

Publication date: 10 May 2021

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

Full work available at URL: https://doi.org/10.1515/anona-2020-0139

zbMATH Keywords

existence of solutionsuniqueness of solutionssystem of Monge-Ampère equations

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Second-order elliptic systems (35J47) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Monge-Ampère equations (35J96)

Related Items (14)

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 ⋮ New results of positive doubly periodic solutions to telegraph equations ⋮ On the solutions to weakly coupled system of \(\boldsymbol{k_i}\)-Hessian equations ⋮ Existence and nonexistence of entire \(k\)-convex radial solutions to Hessian type system ⋮ 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 ⋮ Existence and asymptotic behavior of strictly convex solutions for singular \(k\)-Hessian equations with nonlinear gradient terms ⋮ 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 ⋮ A class of singular \(k_{i}\)-Hessian systems ⋮ Positive solutions of singular multiparameter \(p\)-Laplacian elliptic systems ⋮ A class of singular coupled systems of superlinear Monge-Ampère equations

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