scholarly journals Global regularity for the minimal surface equation in Minkowskian geometry

2011 ◽  
Vol 23 (4) ◽  
Author(s):  
Atanas Stefanov
Keyword(s):  
Minimal Surface ◽  
Global Regularity ◽  
Surface Equation ◽  
Minimal Surface Equation ◽  
Minkowskian Geometry

scholarly journals On the analyticity of generalized minimal surfaces

1971 ◽  
Vol 5 (3) ◽  
pp. 315-320 ◽  
Author(s):  
Neil S. Trudinger
Keyword(s):  
Minimal Surface ◽  
Minimal Surfaces ◽  
Global Regularity ◽  
Regularity Result ◽  
Classical Solutions ◽  
Surface Equation ◽  
Minimal Surface Equation

Strongly differentiable solutions of the minimal surface equation are shown to be classical solutions and consequently locally analytic. A global regularity result is also proved.

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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