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Approximation of Elliptic Equations with Interior Single-Point Degeneracy and Its Application to Weak Unique Continuation Property

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arxiv 2501.10923 v2 pith:KIVXN7PK submitted 2025-01-19 math.AP

Weijia Wu , Yaozhong Hu , Donghui Yang , Jie Zhong This is my paper · ORCID
classification math.AP
keywords approximationcontinuationdegeneracyellipticequationsinteriorpointproperty
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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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  1. Schauder estimates for elliptic equations degenerating on lower dimensional manifolds

    math.AP 2025-01 conditional novelty 7.0 of 10

    Weak solutions to weighted elliptic equations with a distance-to-a-manifold weight are shown to be C^{0,α} or C^{1,α} up to the characteristic manifold under a homogeneous conormal condition.

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