Liouville type theorems for the minimal surface equation in half space

2021 ◽  
Vol 305 ◽  
pp. 270-287
Author(s):  
Guosheng Jiang ◽  
Zhehui Wang ◽  
Jintian Zhu
Keyword(s):  
Minimal Surface ◽  
Half Space ◽  
Liouville Type ◽  
Surface Equation ◽  
Minimal Surface Equation ◽  
Liouville Type Theorems

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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