Capillarity functionals are parameter invariant functionals defined on classes of two-dimensional parametric surfaces in R3 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 S -type minimal surface. Using variational techniques, we prove existence of extremals characterized as saddle-type critical points.
Existence of isovolumetric S2-type stationary surfaces for capillarity functionals / P. Caldiroli, A. Iacopetti. - In: REVISTA MATEMATICA IBEROAMERICANA. - ISSN 0213-2230. - 34:4(2018), pp. 1685-1709. [10.4171/rmi/1040]
Existence of isovolumetric S2-type stationary surfaces for capillarity functionals
A. Iacopetti
2018
Abstract
Capillarity functionals are parameter invariant functionals defined on classes of two-dimensional parametric surfaces in R3 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 S -type minimal surface. Using variational techniques, we prove existence of extremals characterized as saddle-type critical points.
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