The Bieberbach-Rademacher problem for the Monge-Ampère operator

DOI10.1007/BF02567962zbMath0873.35026MaRDI QIDQ5961410

Jerk Matero

Publication date: 8 April 1997

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/156237

zbMATH Keywords

existenceuniquenessblow-up estimatesconvex solution

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65)

Related Items (27)

The Keller-Osserman problem for the k-Hessian operator ⋮ Large solutions to the Monge-Ampère equations with nonlinear gradient terms: existence and boundary 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 ⋮ A unified boundary behavior of large solutions to Hessian equations ⋮ The complex Hessian equation with infinite Dirichlet boundary value ⋮ The iterative properties of solutions for a singular k-Hessian system ⋮ On the Monge-Ampère equation with boundary blow-up: existence, uniqueness and asymptotics ⋮ 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 ⋮ The complex Monge-Ampère equation with infinite boundary value ⋮ On boundary blow-up solutions to equations involving the \(\infty \)-Laplacian ⋮ The blow-up rate of solutions to boundary blow-up problems for the complex Monge-Ampère operator ⋮ 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 ⋮ The Bieberbach-Rademacher problem for the Monge-Ampère operator ⋮ 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 degenerate elliptic equations with non-monotone inhomogeneous terms ⋮ Blow-up solutions to the Monge-Ampère equation with a gradient term: sharp conditions for the existence and asymptotic estimates ⋮ Entire solutions to the Monge-Ampère equation ⋮ On the existence of solutions to the Monge-Ampère equation with infinite boundary values ⋮ Boundary behavior of large solutions to the Monge-Ampère equations with weights ⋮ Boundary behavior of large solutions to a class of Hessian equations

Cites Work

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• Asymptotic behaviour of solutions and their derivatives, for semilinear elliptic problems with blowup on the boundary
• Boundary-blow-up problems in a fractal domain
• On singular boundary value problems for the Monge-Ampère operator
• Quasilinear elliptic equations with boundary blow-up
• On a real Monge-Ampère functional
• On solutions of δu=f(u)
• The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
• On the regularity of the monge-ampère equation det (∂2 u/∂xi ∂xj) = f(x, u)
• On the existence of a complete Kähler metric on non-compact complex manifolds and the regularity of fefferman's equation
• The Bieberbach-Rademacher problem for the Monge-Ampère operator

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