Concentration of cones in the Alt-Phillips problem
Analysis of PDEs
2026-05-12 v2
Abstract
We study minimizing cones in the Alt-Phillips problem when the exponent {\gamma} is close to 1. When {\gamma} converges to 1, we show that the cones concentrate around symmetric solutions to the classical obstacle problem. To be precise, the limiting profiles are radial in a subspace and invariant in directions perpendicular to that subspace.
Cite
@article{arxiv.2503.03626,
title = {Concentration of cones in the Alt-Phillips problem},
author = {Ovidiu Savin and Hui Yu},
journal= {arXiv preprint arXiv:2503.03626},
year = {2026}
}
Comments
Updated the list of references. To appear in ARMA