Elastic catenoids

摘要

We consider the Nitsche functional, which is a linear combination of the area, the Willmore functional and the total Gaufi curvature, on a class of surfaces of revolution with Dirichlet boundary data. We give sufficient conditions on the boundary data for the existence of a regular minimizer, and obtain thereby a solution of the corresponding Euler-Lagrange equation. Moreover we prove that above some threshold boundary value the optimal Nitsche energy is monotonically increasing as a function of the boundary values. Considering symmetric profile curves, we find a minimizer, whose profile curve is monotonically decreasing on the left half, and monotonically increasing on the right half of the interval.