Boundary regularity for solutions of the equation of prescribed Gauss curvature

DOI10.1016/S0294-1449(16)30259-1zbMath0757.35024OpenAlexW2209742881MaRDI QIDQ1187349

John I. E. Urbas

Publication date: 28 June 1992

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIHPC_1991__8_5_499_0

zbMATH Keywords

Hölder continuityGauss curvatureLegendre transformationconvex solutionsfree boundary problem for an auxiliary functiongeneral Monge-Ampère equations

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear elliptic equations (35J60) Free boundary problems for PDEs (35R35)

Related Items (9)

The generalized Dirichlet problem for equations of Monge-Ampère type ⋮ An extremal case of the equation of prescribed Weingarten curvature ⋮ Boundary regularity for solutions of the equation of prescribed Gauss curvature ⋮ \(P\)-capacity vs surface-area ⋮ Unnamed Item ⋮ Curvature flow with a general forcing term in Euclidean spaces ⋮ A logarithmic Gauss curvature flow and the Minkowski problem. ⋮ A non-homogeneous elliptic problem dealing with the level set formulation of the inverse mean curvature flow ⋮ Inscribed radius estimates for inverse curvature flow in sphere and hyperbolic space

Cites Work

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• On the regularity of the monge-ampère equation det (∂2 u/∂xi ∂xj) = f(x, u)

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