On the Capillary Surface in a Wide Circular Tube

Abstract

An explicit asymptotic formula for the wide circular tube is proved. The leading term defines the capillary surface over the half plane with the given boundary contact angle. An explicit estimate of the remainder uniform with respect to the boundary contact angle and the radius of the tube is given. This uniform behaviour is caused by the strong non-linearity of the problem and has no counterpart for linear problems. The proof of the main result is based on a maximum principle and on a mapping which brings the right parameter of development onto the right place of the equation.