Isoperimetric cones and minimal solutions of partial overdetermined problems
Analysis of PDEs
2019-05-27 v1
Abstract
In this paper we consider a partial overdetermined mixed boundary value problem in domains inside a cone as in [18]. We show that in cones having an isoperimetric property the only domains which admit a solution and which minimize a torsional energy functional are spherical sectors centered at the vertex of the cone. We also show that cones close in the -metric to an isoperimetric one are also isoperimetric, generalizing so a result of [1]. This is achieved by using a characterization of constant mean curvature polar graphs in cones which improves a result of [18].
Cite
@article{arxiv.1905.10139,
title = {Isoperimetric cones and minimal solutions of partial overdetermined problems},
author = {Filomena Pacella and Giulio Tralli},
journal= {arXiv preprint arXiv:1905.10139},
year = {2019}
}