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

DOI10.4171/RMI/1040zbMATH Open1411.53011arXiv1608.01150OpenAlexW2902299574MaRDI QIDQ1725562

Alessandro Iacopetti, Paolo Caldiroli

Publication date: 14 February 2019

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

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 S2-type minimal surface. Using variational techniques, we prove existence of extremals characterized as saddle-type critical points.

Full work available at URL: https://arxiv.org/abs/1608.01150

zbMATH Keywords

variational methodsisoperimetric problemsparametric surfacesH-bubbles

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Existence theories for free problems in two or more independent variables (49J10)

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Isovolumetric and isoperimetric problems for a class of capillarity functionals

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