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arXiv · 2501.10923

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
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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.

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Weijia Wu, Yaozhong Hu, Donghui Yang, Jie Zhong. 2025-01-19. Approximation of Elliptic Equations with Interior Single-Point Degeneracy and Its Application to Weak Unique Continuation Property. https://arxiv.org/abs/2501.10923

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