scholarly journals Numerical study of the discrete minimal surface equation in a nonconvex domain

1973 ◽  
Author(s):  
P. Concus
Keyword(s):  
Minimal Surface ◽  
Numerical Study ◽  
Surface Equation ◽  
Minimal Surface Equation ◽  
Nonconvex Domain

scholarly journals For the minimal surface equation, the set of solvable boundary values need not be convex

1996 ◽  
Vol 53 (3) ◽  
pp. 369-372
Author(s):  
Frank Morgan
Keyword(s):  
Minimal Surface ◽  
Smooth Domain ◽  
Boundary Values ◽  
Surface Equation ◽  
Minimal Surface Equation

One might think that if the minimal surface equation had a solution on a smooth domain D ⊂ Rn with boundary values φ, it would have a solution with boundary values tφ for all 0 ≤ t ≤ 1. We give a counterexample in R2.

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