Boundary Behavior of a Nonparametric Surface of Prescribed Mean Curvature Near a Reentrant Corner

DOI10.2307/2000545zbMath0602.35042OpenAlexW4231422266MaRDI QIDQ3737858

Alan R. Elcrat, Kirk E. Lancaster

Publication date: 1986

Full work available at URL: https://doi.org/10.2307/2000545

zbMATH Keywords

Dirichlet problemboundary behaviorreentrant cornerradial limitsprescribed mean curvaturenonparametric surface

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Nonlinear boundary value problems for linear elliptic equations (35J65) Boundary values of solutions to elliptic equations and elliptic systems (35J67) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Variational methods for second-order elliptic equations (35J20)

Related Items (10)

Behavior of a bounded non-parametric \(H\)-surface near a reentrant corner ⋮ Behavior of prescribed mean curvature hypersurfaces on reentrant ridges ⋮ Existence and Nonexistence of Radial Limits of Minimal Surfaces ⋮ A generalization of ``Existence and behavior of the radial limits of a bounded capillary surface at a corner ⋮ Radial limits of nonparametric PMC surfaces with intermediate boundary curvature ⋮ On a minimal hypersurface in \(\mathbb{R}^4 \) ⋮ Boundary behavior near reentrant corners for solutions of certain elliptic equations ⋮ Boundary continuity of nonparametric prescribed mean curvature surfaces ⋮ Radial limits of capillary surfaces at corners ⋮ Boundary behavior of rotationally symmetric prescribed mean curvature hypersurfaces in \(\mathbb{R}^4\)

Cites Work

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• On the equation of surfaces of prescribed mean curvature. Existence and uniqueness without boundary conditions
• Remarks relevant to minimal surfaces and to surfaces of prescribed mean curvature
• Über das Randverhalten quasilinearer elliptischer Systeme mit isothermen Parametern
• Gradient estimates and mean curvature
• BOUNDARY BEHAVIOR OF A NON-PARAMETRIC MINIMAL SURFACE IN ℝ3 AT A NON-CONVEX POINT
• Local estimates for gradients of solutions of non‐uniformly elliptic and parabolic equations
• The Dirichlet Problem for Surfaces of Constant Mean Curvature

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