Stability inequalities for one-phase cones
Analysis of PDEs
2026-01-26 v1 Differential Geometry
Abstract
We obtain strict stability inequalities for homogeneous solutions of the one-phase Bernoulli problem. We prove that in dimension and above, cohomogeneity one solutions with bi-orthogonal symmetry are strictly stable. As a consequence, we obtain a bound on the first eigenvalue and the decay rates of Jacobi fields, with applications to the generic regularity of the one-phase problem.
Cite
@article{arxiv.2601.16966,
title = {Stability inequalities for one-phase cones},
author = {Benjy Firester and Raphael Tsiamis and Yipeng Wang},
journal= {arXiv preprint arXiv:2601.16966},
year = {2026}
}