Approximation of Elliptic Equations with Interior Single-Point Degeneracy and Its Application to Weak Unique Continuation Property
Weijia Wu, Yaozhong Hu, Donghui Yang, Jie Zhong
公開日: 2025/1/19
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.