The following image is from the book "Regularity Theory for Mean Curvature Flow", by Ecker.
I consider the plateau problem, whose goal is to solve minimal surface given fixed boundary values.
In the case of radially symmetrical case, I wonder what shape the minimal surface is if
the boundary is $u(x)=f(r)=b$ when $r$ is the largest radius.
For example, if I implement this by using gradient descent, I set the following as initial guess:
the boundary value: $f(r_{end})=1$ and other values $f(r)=0$,
what shape the minimal surface should it be?
The following figure is an intermediate result of my implementation. The x axis denotes 'r' (from 0 to 1) and the y axis denotes $f(r)$. Does this result make sense?
