Approximation of Elliptic Equations with Interior Single-Point Degeneracy and Its Application to Weak Unique Continuation Property
Analysis of PDEs
2025-09-03 v2
Abstract
This paper investigates the quantitative weak unique continuation property (QWUCP) for a class of high-dimensional elliptic equations with interior point degeneracy. First, we establish well-posedness results in weighted function spaces. Then, using an innovative approximation method, we derive the three-ball theorem at the degenerate point. Finally, we apply the three-ball theorem to prove QWUCP for two different cases.
Keywords
Cite
@article{arxiv.2501.10923,
title = {Approximation of Elliptic Equations with Interior Single-Point Degeneracy and Its Application to Weak Unique Continuation Property},
author = {Weijia Wu and Yaozhong Hu and Donghui Yang and Jie Zhong},
journal= {arXiv preprint arXiv:2501.10923},
year = {2025}
}