Quantitative Weak Unique Continuation on Annular Domains for Backward Degenerate Parabolic Equations with Degenerate Interior Points
Analysis of PDEs
2026-05-05 v1 Optimization and Control
Abstract
In this paper, we establish a quantitative weak unique continuation theorem on an annular domain for a backward degenerate parabolic equation with a degenerate interior point. Our methodology hinges on approximating the solution of the degenerate parabolic equation through solutions of non-degenerate parabolic counterparts. Subsequently, we establish Carleman estimates for the non-degenerate parabolic equation across two separate domains. By virtue of these estimates, we deduce a quantitative weak unique continuation property for the degenerate parabolic equation, thereby substantiating the weak unique continuation result for the original degenerate parabolic equation.
Keywords
Cite
@article{arxiv.2605.02797,
title = {Quantitative Weak Unique Continuation on Annular Domains for Backward Degenerate Parabolic Equations with Degenerate Interior Points},
author = {Dong-Hui Yang and Bao-Zhu Guo and Guojie Zheng and Jie Zhong},
journal= {arXiv preprint arXiv:2605.02797},
year = {2026}
}