Some existence results and gradient estimates of solutions of the Dirichlet problem for the constant mean curvature equation in convex domains

DOI10.1006/JDEQ.2001.4050zbMath1257.35093OpenAlexW2083756346MaRDI QIDQ1604639

Jaime Bruck Ripoll

Publication date: 8 July 2002

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jdeq.2001.4050

zbMATH Keywords

Dirichlet problemconstant mean curvatureexistence resultsconvex domainsgradient estimates

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Nonlinear elliptic equations (35J60)

Related Items (5)

CMC graphs with planar boundary in \(\mathbb{H}^2\times \mathbb{R}\) ⋮ WETTING PHENOMENA AND CONSTANT MEAN CURVATURE SURFACES WITH BOUNDARY ⋮ Height estimates for graph parametrized surfaces ⋮ Existence of a BV solution for a mean curvature equation ⋮ Existence and uniqueness of CMC parabolic graphs in \(\mathbb H^3\) with boundary data satisfying the bounded slope condition

Cites Work

• Unnamed Item
• The Dirichlet problem for the minimal surface equation on unbounded planar domains
• On the image of the Gauss map of an immersed surface with constant mean curvature in \(\mathbb{R}^3\)
• On the bounded slope condition
• Le problème de Dirichlet pour l'équation des surfaces minimales sur des domaines non bornés
• Some maximum principles for nonlinear elliptic equations in divergence form with applications to capillary surfaces and to surfaces of constant mean curvature
• The Dirichlet Problem for Surfaces of Constant Mean Curvature
• Some characterization, uniqueness and existence results for Euclidean graphs of constant mean curvature with planar boundary.

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