Radial limits of bounded nonparametric prescribed mean curvature surfaces

Mozhgan Entekhabi, Kirk Lancaster
2016 Pacific Journal of Mathematics  
Consider a solution f∈ C^2(Ω) of a prescribed mean curvature equation div(∇ f/√(1+|∇ f|^2))=2H(x,f) in Ω, where Ω⊂^2 is a domain whose boundary has a corner at O=(0,0)∈∂Ω. If _x∈Ω |f(x)| and _x∈Ω |H(x,f(x))| are both finite and Ω has a reentrant corner at O, then the radial limits of f at O, Rf(θ) _r↓ 0 f(rcos(θ),rsin(θ)), are shown to exist and to have a specific type of behavior, independent of the boundary behavior of f on ∂Ω. If _x∈Ω |f(x)| and _x∈Ω |H(x,f(x))| are both finite and the trace
more » ... of f on one side has a limit at O, then the radial limits of f at O exist and have a specific type of behavior.
doi:10.2140/pjm.2016.283.341 fatcat:xemxc2olljdvxnfjblmlnlrruy