A note on the spatial decay of a three-dimensional minimal surface over a semi-infinite cylinder
The author extends to solutions of the three-dimensional minimal surface equation for a semi-infinite cylinder with a simply-connected and convex section some estimates concerning the spatial decay at infinity for solutions of the two-dimensional equation on a strip due to Knowles (cf. references). Roughly speaking, the result says that solutions decay exponentially in the third variable at least as fast as do solutions of Laplace's equation. The proof is carried out by using a comparison theorem for second order nonlinear equations.
three-dimensional minimal surface equation
scientific article; zbMATH DE number 3937619