The Dirichlet problem for the equation of prescribed Gauss curvature

DOI10.1017/S000497270002089XzbMath0524.35047MaRDI QIDQ3037904

Neil S. Trudinger, John I. E. Urbas

Publication date: 1983

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Dirichlet problemexistenceprescribed Gauss curvatureunique convex solutiona priori gradient estimateequations of Monge-Ampere type

Mathematics Subject Classification ID

Related Items (42)

The generalized Dirichlet problem for equations of Monge-Ampère type ⋮ L^pand Hölder estimates for a class fo degenerate elliptic boundary value problems Application to the Monge–Amp ére equation ⋮ The Dirichlet problem for the prescribed curvature equations ⋮ Isoperimetric inequalities for quermassintegrals ⋮ Nonlinear oblique boundary value problems for Hessian equations in two dimensions ⋮ Dirichlet problem for the equation of a given Lorentz-Gaussian curvature ⋮ The dirichlet problem for a class of fully nonlinear elliptic equations ⋮ On the solvability of the Dirichlet problem for degenerate equations of Monge-Ampere type ⋮ Global regularity for a class of Monge-Ampère type equations with nonzero boundary conditions ⋮ Global Hölder estimates for equations of Monge-Ampère type ⋮ Comparison principles for weak solutions of monge–ampere equations ⋮ Boundary lower estimates for a class of fully nonlinear elliptic partial differential equations ⋮ Boundary estimates for solutions of the Monge-Ampère equation satisfying Dirichlet-Neumann type conditions in annular domains ⋮ Convergent approximation of non-continuous surfaces of prescribed Gaussian curvature ⋮ Boundary regularity for \(k\)-Hessian equations ⋮ Sharp boundary regularity for some degenerate-singular Monge-Ampère equations on \(k\)-convex domain ⋮ \(\mathbb R\)-mapping based method for designing of form cutting tool for sculptured surface machining. ⋮ A priori bounds and necessary conditions for solvability of prescribed curvature equations ⋮ Monge-Ampère equations on the nonstrict convex domains ⋮ On the solvability of some monge-ampère equations ⋮ On the Monge-Ampère equation with boundary blow-up: existence, uniqueness and asymptotics ⋮ Boundary regularity for solutions of the equation of prescribed Gauss curvature ⋮ On Monge-Ampère equations with nonlinear gradient terms -- infinite boundary value problems ⋮ On solvability conditions of the Dirichlet problem for \(m\)-curvature equations ⋮ On the solvability of Monge-Ampère type equations in non-uniformly convex domains ⋮ \(C^ 2\) a priori estimates for degenerate Monge-Ampère equations ⋮ A priori estimates for quasilinear equations related to the Monge-Ampère equation in two dimensions ⋮ Existence of multiple solutions to the equations of Monge-Ampère type ⋮ Unnamed Item ⋮ Interior curvature bounds for a class of curvature equations ⋮ Symmetry results for classical solutions of Monge-Ampère systems on bounded planar domains ⋮ Regularity of degenerate Monge-Ampère and prescribed Gaussian curvature equations in two dimensions ⋮ \(C^{1,1}\) regularity for solutions to the degenerate \(L_p\) dual Minkowski problem ⋮ Boundary Hölder regularity for a class of fully nonlinear elliptic partial differential equations ⋮ Existence of Global Smooth Solutions to Dirichlet Problem for Degenerate Elliptic Monge–Ampere Equations ⋮ The regularity of the surface of the Gauss curvature \(0\leqq K\in C_0^\infty\) ⋮ On the Dirichlet problem for degenerate Monge-Ampère type equations ⋮ On the Dirichlet problem for degenerate Monge-Ampère equations. ⋮ The Dirichlet problem for the degenerate elliptic Monge-Ampère equation ⋮ Surfaces with prescribed curvature. I ⋮ The Dirichlet problem for prescribed principal curvature equations ⋮ Global regularity for a class of Monge-Ampère type equations

Cites Work

• Unnamed Item
• Equations de Monge-Ampère réelles
• Sur les équations de Monge-Ampère. I
• Fully Nonlinear, Uniformly Elliptic Equations Under Natural Structure Conditions
• On the regularity of the monge-ampère equation det (∂2 u/∂xi ∂xj) = f(x, u)
• The problem of dirichlet for quasilinear elliptic differential equations with many independent variables

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