Abstract and Applied Analysis
Volume 1 (1996), Issue 3, Pages 291-304

Bifurcation of the equivariant minimal interfaces in a hydromechanics problem

A. Y. Borisovich and W. Marzantowicz

Institute of Mathematics, University of Gdańsk, ul. Wita Stwosza 57, Gdańsk 80-952, Poland

Received 16 April 1996

Copyright © 1996 A. Y. Borisovich and W. Marzantowicz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this work we study a deformation of the minimal interface of two fluids in a vertical tube under the presence of gravitation. We show that a symmetry of the base of tube let us to apply a method developed earlier by the first author and based on the Crandall-Rabinowitz bifurcation theorem. Using the natural symmetry of the corresponding variational problem defined by a symmetry of region and restricting the functional to spaces of invariant functions we show the existence of bifurcation, and describe its local picture, for interfaces parametrized by the square and disc.