Approximation of elliptic equations with interior single-point degeneracy and its application to weak unique continuation property

¹ School of Mathematics and Physics, North China Electric Power University, Beijing, 102206, China
² Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2G1, Canada
³ School of Mathematics and Statistics, Central South University, Changsha, 410083, China
⁴ Department of Mathematics, California State University Los Angeles, Los Angeles, CA 90032, USA

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 8 August 2025
Accepted: 20 February 2026

Abstract

This paper investigates the weak unique continuation property (WUCP) 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 sphere inequality at the degenerate point. Finally, we apply the three sphere inequality to prove WUCP for two different cases.