We prove a rigidity result for Serrin's overdetermined problem in a cone that is contained in a half-space in arbitrary dimensions. In the special case where the cone is an epigraph, this result was shown previously in low dimensions with a different approach.
@article{arxiv.1707.05460,
title = {On a partially overdetermined problem in a cone},
author = {Christos Sourdis},
journal= {arXiv preprint arXiv:1707.05460},
year = {2017}
}