The Perron method and the non-linear Plateau problem

DOI10.1007/s10711-012-9742-0zbMath1271.53056arXiv0912.2892OpenAlexW2963682431MaRDI QIDQ357841

Mohammad Hasan, M. Dambrine

Publication date: 13 August 2013

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.2892

zbMATH Keywords

Monge-Ampère equationPerron methodGaussian curvaturePlateau's problemnon linear elliptic PDEs

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Nonlinear elliptic equations (35J60) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (2)

Starshaped locally convex hypersurfaces with prescribed curvature and boundary ⋮ Pseudoconvexity for the special Lagrangian potential equation

Cites Work

• Dirichlet duality and the nonlinear Dirichlet problem on Riemannian manifolds
• The existence of hypersurfaces of constant Gauss curvature with prescribed boundary.
• Special Lagrangian curvature
• Locally convex hypersurfaces of constant curvature with boundary
• Dirichlet duality and the nonlinear Dirichlet problem
• Nonlinear second-order elliptic equations V. The dirichlet problem for weingarten hypersurfaces
• User’s guide to viscosity solutions of second order partial differential equations

This page was built for publication: The Perron method and the non-linear Plateau problem