scholarly journals A Bernstein-type result for the minimal surface equation

2015 ◽  
pp. 1231-1237
Author(s):  
Alberto Farina
Keyword(s):  
Minimal Surface ◽  
Type Result ◽  
Bernstein Type ◽  
Surface Equation ◽  
Minimal Surface Equation

scholarly journals Symmetric solutions of the singular minimal surface equation

2021 ◽  
Author(s):  
Ulrich Dierkes ◽  
Nico Groh
Keyword(s):  
Minimal Surface ◽  
Bernstein Type ◽  
Surface Equation ◽  
Minimal Surface Equation ◽  
Singular Minimal Surface

AbstractWe classify all rotational symmetric solutions of the singular minimal surface equation in both cases $$\alpha <0$$ α < 0 and $$\alpha >0$$ α > 0 . In addition, we discuss further geometric and analytic properties of the solutions, in particular stability, minimizing properties and Bernstein-type results.

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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