Existence of nonradial domains for overdetermined and isoperimetric problems in nonconvex cones
Analysis of PDEs
2022-07-06 v1
Abstract
In this work we address the question of the existence of nonradial domains inside a nonconvex cone for which a mixed boundary overdetermined problem admits a solution. Our approach is variational, and consists in proving the existence of nonradial minimizers, under a volume constraint, of the associated torsional energy functional. In particular we give a condition on the domain on the sphere spanning the cone which ensures that the spherical sector is not a minimizer. Similar results are obtained for the relative isoperimetric problem in nonconvex cones.
Keywords
Cite
@article{arxiv.2111.09817,
title = {Existence of nonradial domains for overdetermined and isoperimetric problems in nonconvex cones},
author = {Alessandro Iacopetti and Filomena Pacella and Tobias Weth},
journal= {arXiv preprint arXiv:2111.09817},
year = {2022}
}