PreprintarXiv licencearXiv
Non-degeneracy and local uniqueness of bubbling solutions for a singular Liouville equation
Abstract
We consider the following singular Liouville equation $-Δv=λV(x)|x|^2e^v \quad \text{in } B_1, \quad v=0 \quad \text{on } \partial B_1, $ where B1⊂ℝ2 is the unit disk, λ>0 is a small parameter, and V is a positive smooth function. We first prove a non-degeneracy result for the bubbling solutions constructed in \cite{D-W-Z2026} by the local Pohozaev identities. Then we use this non-degeneracy result to establish the local uniqueness of bubbling solutions whose concentration parameters are sufficiently close.
Related
- Asymptotic analysis and uniqueness of blowup solutions of non-quantized singular mean field equations
- Sharp non-uniqueness of singular solutions to the one-dimensional periodic cubic nonlinear Schrödinger equation
- Sign-changing bubbling solutions on polygons for the Brezis-Nirenberg problem in high dimensions
- Radial Symmetry and Nondegeneracy for Singular Liouville Systems with Small Singular Exponents
- Liouville-type theorems and perturbation uniqueness for stationary incompressible MHD with directional fractional dissipation
BibTeX
@misc{guo2026nondegeneracy,
title = {{Non-degeneracy and local uniqueness of bubbling solutions for a singular Liouville equation}},
author = {Yuxia Guo and Jionghao Lv},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34815},
eprint = {2609.34815},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34815},
}
RIS
TY - UNPB
TI - Non-degeneracy and local uniqueness of bubbling solutions for a singular Liouville equation
AU - Yuxia Guo
AU - Jionghao Lv
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.34815
UR - https://arxiv.org/abs/2609.34815
AB - We consider the following singular Liouville equation $-Δv=λV(x)|x|^2e^v \quad \text{in } B_1, \quad v=0 \quad \text{on } \partial B_1, $ where B_1⊂ℝ^2 is the unit disk, λ>0 is a small parameter, and V is a positive smooth function. We first prove a non-degeneracy result for the bubbling solutions constructed in \cite{D-W-Z2026} by the local Pohozaev identities. Then we use this non-degeneracy result to establish the local uniqueness of bubbling solutions whose concentration parameters are sufficiently close.
ER -