Serrin problems with vertical boundary behavior
Analysis of PDEs
2026-07-21 v1
Abstract
We study Serrin-type overdetermined problems for a class of possibly degenerate elliptic operators under a vertical boundary condition forcing gradient blow-up. We identify the precise regime in which the problem admits a solution on a ball. In this regime, we prove rigidity: every solution domain is a ball, and the solution is uniquely determined by an explicit radial profile.
Cite
@article{arxiv.2607.18952,
title = {Serrin problems with vertical boundary behavior},
author = {Julián Pozuelo and Simone Verzellesi},
journal= {arXiv preprint arXiv:2607.18952},
year = {2026}
}