Revista Matemática Iberoamericana


Full-Text PDF (346 KB) | Metadata | Table of Contents | RMI summary
Volume 34, Issue 4, 2018, pp. 1685–1709
DOI: 10.4171/rmi/1040

Published online: 2018-12-03

Existence of isovolumetric $\mathbb S^2$-type stationary surfaces for capillarity functionals

Paolo Caldiroli[1] and Alessandro Iacopetti[2]

(1) Università degli Studi di Torino, Italy
(2) Università degli Studi di Torino, Italy

Capillarity functionals are parameter invariant functionals defined on classes of two-dimensional parametric surfaces in $\mathbb R^3$ as the sum of the area integral and a non homogeneous term of suitable form. Here we consider the case of a class of non homogenous terms vanishing at infinity for which the corresponding capillarity functional has no volume-constrained $\mathbb S^2$-type minimal surface. Using variational techniques, we prove existence of extremals characterized as saddle-type critical points.

Keywords: Isoperimetric problems, parametric surfaces, variational methods, $H$-bubbles

Caldiroli Paolo, Iacopetti Alessandro: Existence of isovolumetric $\mathbb S^2$-type stationary surfaces for capillarity functionals. Rev. Mat. Iberoam. 34 (2018), 1685-1709. doi: 10.4171/rmi/1040