Stable cones in the Alt-Phillips free boundary problem

Aram Karakhanyan; Tomás Sanz-Perela

doi:10.1007/s00526-026-03251-2

Stable cones in the Alt-Phillips free boundary problem

Aram Karakhanyan
, Tomás Sanz-Perela

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we prove a classification result for axially symmetric one-phase stable solutions of the Alt-Phillips free boundary problem in the range γ∈(0,2/3). We show that such solutions are one-dimensional in dimensions 3, 4, and 5 for a range of γ depending on the dimension. To accomplish this, we establish a stability inequality that extends the one for the Alt-Caffarelli problem (γ=0) to the whole range γ∈(0,2).

Original language	English
Article number	83
Journal	Calculus of Variations and Partial Differential Equations
Volume	65
Issue number	3
Early online date	17 Feb 2026
DOIs	https://doi.org/10.1007/s00526-026-03251-2
Publication status	Published - 31 Mar 2026

Keywords / Materials (for Non-textual outputs)

math.AP

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10.1007/s00526-026-03251-2

2403.13059v2Accepted author manuscript, 359 KB

https://arxiv.org/abs/2403.13059

Mean curvature measure of free boundary
Karakhanyan, A. (Principal Investigator)
EPSRC
1/03/20 → 29/02/24
Project: Research

Cite this

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AB - In this paper we prove a classification result for axially symmetric one-phase stable solutions of the Alt-Phillips free boundary problem in the range γ∈(0,2/3). We show that such solutions are one-dimensional in dimensions 3, 4, and 5 for a range of γ depending on the dimension. To accomplish this, we establish a stability inequality that extends the one for the Alt-Caffarelli problem (γ=0) to the whole range γ∈(0,2).

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Stable cones in the Alt-Phillips free boundary problem

Abstract

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Mean curvature measure of free boundary

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