Axisymmetric p-harmonic modes in circular cones: nodal classification and two-term asymptotics
A non-peer-reviewed mathematical preprint on homogeneous axisymmetric p-harmonic functions in circular cones. The complete original PDF and author attribution are retained.
GitHub report and source · Hugging Face · Zenodo
Authors: Kadyrbekov, Khamit, Kadirbekov, Daniyal.
We study homogeneous axisymmetric solutions of the p-Laplace equation in a circular cone with zero lateral boundary values. A lifted phase gives one positive and one negative homogeneity exponent for each nodal index. An energy argument excludes an additional continuously differentiable profile vanishing at the axis. We obtain two-term high-index asymptotics, including an axis-layer phase shift given by a convergent improper integral. The two branches have opposite leading terms and an explicit limiting sum. The analysis concerns the axisymmetric class and does not provide an expansion of an arbitrary solution at a conical point. Non-peer-reviewed preprint, version 1.0.
Complete published manuscript · Original Zenodo record.
Existing manuscript license: CC BY 4.0. This is a mirror of the published preprint, not a new experiment or a peer-review claim.
Publication record
This page was added on 14 September 2026 to align the public archive. The original report, source history and licensing remain available from the links above. AI-assisted archival preparation.